Science of the Absolute Chapter 2 - Prologue
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Created on Monday, 20 October 2008 19:07
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Published on Monday, 20 October 2008 19:07
Written by Patrick Misson
AN INTEGRATED SCIENCE OF THE ABSOLUTE
Epistemology, methodology and axiology presuppose one another in the total sense of the term "Methodology". As applicable to this chapter, this term requires some explanation. Each discipline or branch of scientific thinking aiming at certainty presupposes a methodology. There should be an agreement between the object of research and the subject who conducts the enquiry along the most fruitful and significant channels of research. There is a subject-matter and an object-matter which have to be put into a direct bipolar relation if the methodology is to be correct.
In the present work we are concerned with a Science of the Absolute and the wholesale methods of attaining the truth of the Absolute. The modern tendency is not to stress this wholesale aspect but to be less ambitious and to seek truth by piecemeal methods of trial and error. Logical positivists prefer to look upon scientific method in this fashion. As each discipline must have a proper method for attaining the knowledge which is its object, it is fully scientific even in a modern sense, to think of a wholesale approach to the study of the Absolute. Therefore we shall dispense here with the usual inductive and deductive approaches proper only to specific branches of knowledge. The detailed subdivisions of method, such as the inductivo-hypothetical, the historical or genetic, the descriptive or the analytic approaches, when unilaterally understood need not concern us here. The bilateral dialectical and axiological approach agrees with the methodology of this chapter, where a negative or descending reduction or cancellation of counterparts, tending to abolish plurality and relativity in favour of a unity and an absolute resultant certitude or validity are to be kept in mind.
In the first chapter it was supposed that the outer world, as given to the senses, was real. Here the relation between subject and object tends to become more subjectively verticalized. The two counterparts belong more closely to each other, as the Absolute can neither be conceived pluralistically nor dualistically because of the tautology or contradiction that would then result.
The first task that we have to undertake in the present chapter is to reduce relativity and multiplicity so as to abolish them in the name of the One Absolute. The relativistic features seemingly tolerated in the first chapter have now to be revised into unitive and absolutist terms. This task is mainly one of reduction by the well-known method of the Upanishads called neti-neti (not this, not this) or Nivritti Marga. This is known in the West as the negative way and is very often used by the mystics. When the process of reduction has been fully accomplished, there is an element of reconstruction of the finalized position in respect of the central subject-matter of the work. Such is, in broad outline, the scope and content of the present chapter. The methodology belonging to such a context has not only to be wholesale and subjective in approach, but also one that belongs to the context of directing human understanding along lines that yield the greatest clarity and certitude in respect of the totality of truth and reality.
1. METHODOLOGY AND STRUCTURALISM
The definition of methodology found in Rune's Dictionary of Philosophy is as follows:
"The systematic analysis and organization of the rational and experimental principles and processes which must guide a scientific inquiry, or which constitute the structure of the special sciences more particularly." (1)
Further on we read:
"Thus, methodology is a generic term exemplified in the specific method of each science .... In the last resort, methodology results from the adjustment of our mental powers to the love and pursuit of truth." (2)
From a perusal of this apparently sinuous definition it is evident that the clarification itself needs further explanation. Besides being related to epistemology, there is the question of structure, a term which is becoming popular in the West at present.
This reference to structure is made in more than one context in the definition of methodology. The final summing up of the position unmistakably points to the necessity of relating the subject and object as counterparts that belong together to one and the same total knowledge-situation. We shall not be too far removed from the correct meaning of methodology when we state here that there is both an objective structuralism implied in positive truth as well as a corresponding negative structuralism in the mind of the person who seeks to find the truth. Methodology is concerned with the correct way of research in making the Self relate itself to its own counterpart, the non-Self. It is in the overall context of the central, neutral and normative Self always acting as a reference that a correct methodology, as understood in the above manner, attains its purpose, which is that of a certitude given at one and the same time to intuition as well as to reason or common sense.
Before passing on to other philosophers we shall devote some more space to a closer examination of the implications of Cartesian methodology. We shall not enter into an enumeration of all the aspects of method indicated in Descartes' "Discourse on Method and Meditations on First Philosophy". Descartes was an expert in optics, mathematics and logic. As the father of modern philosophy, all his elaborations follow an overall vision of reality, revealing the same structural implications, whatever might be the particular discipline by which he proposes to examine the absolute substance he is always concerned with. The two broad divisions of Cartesianism are known as res cogitans (thinking substance) and res extensa (extended substance). They belong to one and the same substance having its own structure represented by the same correlates.
Whether Descartes had the intention of applying a more general and extrapolated version of this structural plan of correlates to the larger domains of philosophical speculation has not been sufficiently clarified in his writings. Yet the so-called rationalist philosophers like Spinoza, Leibniz and others can easily be recognized as continuators of the Cartesian tradition, at least in the matter of postulating something like a thinking substance or monad. The schematismus of Kant can be traced back to the correlates when it is more mathematically and statically understood, and forwards to Bergson's notion of the élan vital which submits to a schéma moteur serving as the basis of his creative evolution. The schematismus attains finality in. the hands of Eddington where the new epistemological structuralism of the philosophy of science is introduced. We have examined elsewhere this movement underlying modern thought. (3)
It was Cartesianism that set the ball rolling in this direction. Descarte´s method is misunderstood as accepting rather arbitrarily and artificially a form of dualism between the mechanistic and the living aspects. This was because he did not properly explain how they could belong together. A more careful study of his writings reveals that the main implications of his philosophy have always remained the same fundamental features of the structuralism originally implied in his correlates. Spinoza also defined absolute substance treated with its accidents or attributes on similar lines. This in turn gave place to the Monad of monads of Leibniz. Kant's ding-an-sich is not different from Descartes' absolute susbstance and could be taken to refer to the same.
The broad features of this structuralism are however, sufficiently evident in Descartes' writings. Besides these notions of substance there is also the tabula rasa of Locke and Hume's phenomenological reality. All these are meant to be normative notions of the Absolute viewed from possible cosmological, psychological or philosophical angles. The particular point of view of Descartes in respect of this normative notion is such that his epistemology and axiology provide a clear-cut methodology with its structural outlines fully in evidence. It is time that this particular structural methodology was more fully used.
2. FURTHER IMPLICATIONS OF CARTESIANISM
It will be convenient for us to start with the notion of animal spirits, which Descartes recognized as a kind of mental substance or emanation wherein psychological and cosmological factors co-exist. This makes for the interaction of the body and the mind. In his cosmology the same absolute substance is the basis for what he called vortices which express their divisibility, figurability or mobility so as to bring into existence various objective entities. A kind of thinking substance similar to Spinoza's is implied here, although Descartes works out the cosmological implications in greater detail so as to make his position a continental rival to the more rigidly or radically conceived cosmology of Newton.
Instead of straight lines and laws of motions, we have in Descartes' view curvatures of space, without which his vortices could not be thought of. These vortices have at least the curvature in common with what other philosophers, like Bergson, have referred to in terms of a vermicular spiral which shares the features of a logarithmic spiral. Bergson also refers to a helicoidal movement involving space and time. Whatever the shape involved, the cosmology of Descartes lays the foundation of the notion of an absolute substance which could be referred to in terms of his two correlates These correlates have unmistakable structural implications whose epoch making significance is proved by their growing use in every department of modern science.
Whether Descartes himself established a direct relation between these correlates belonging to the context of his analytical geometry and his two famous divisions of reality (i.e. res cogitans and res extensa) or not, it is nonetheless quite legitimate for us to recommend their extrapolated use in the manner we have outlined.
The thinking of the Absolute substance is referable to the vertical axis which answers to all possible cogitations of the mind, while the other correlate refers to pure a priori space schematically understood, as with the philosophy of Kant where extension constitutes a self-evident or a priori essence of reality where extension has a horizontal reference. Thus res extensa refers to the horizontal spatialized essence while res cogitans refers to its verticalized counterpart, combining mind and matter into one absolute reality. This would not have been possible if Cartesianism implied a merely dualistic philosophy which did not postulate such an absolute thinking substance.
Descartes is content to call this substance a form of animal spirit and in doing this his position is not radically different from that of Bergson who insists on the fluid character of the substance in his notion of the ' élan vital '. The process of creative becoming is more important for Bergson, but the status of the animal spirit of Descartes remains, in principle at least, the same as his own ' élan vital '. Descartes was more of a mathematician whereas Bergson was more of a biologist. Such differences of bias however, are not important for us in our present task of extracting the broad features of structuralism common to the methodology of both these philosophers. For both of them there is a neutral and monistic substance which can be submitted to the two basic references of the cartesian correlates. The process involved in the participation of space and time, or extension and thought, reveals the same kind of vermicular spiral or figure-of-eight, not unlike the vortices mentioned by Descartes.
Overlooking the details that such a structure represents, we can, even at this stage, see the broad outlines of the structuralism anticipated and presupposed by Descartes.
If we keep these features in mind, it will be easy for us to fit into the same picture the three basic types of ideas implied in Cartesianism which are: the innate, the adventitious and the factitious. The first mentioned class of all self-evident ideas belongs naturally to the bottom of the vertical axis, and the last one to the top of the same axis, because facts must also have a horizontal reference because they constitute what is called sensa or sensible realities "out there" with a spatial rather than a pure inner reference.
The status of the second type of idea (i.e. the adventitious) has been questioned or doubted by the critics of Descartes who thought there was something ambiguous or uncertain implied in it. An uncertainty principle is in fact inevitable even in modern scientific thinking. Therefore the questionability of the adventitious ideas of Descartes can no longer be considered a weak point in Cartesian epistemology. Uncertainty is an. admissible form of scientific certitude at present. When we admit into our logic the principle of non-contradiction, without the principle of the excluded middle, we make room for entities that are not definable from one point of view or its opposite. Vedanta recognizes this as the principle of non-predictability (anirvacaniya). Non-predicability is therefore a strong point rather than a weak one in Cartesian methodology.
When Descartes says that his three categories of ideas are self-evident he merely underlines their a priori status, just as Kant does in his notion of schematized space. It is a conceptualized version which. counts here, and Eddington readily recognized this when he said it was concepts rather than percepts that matter.
The animal spirit as an absolute substance is where innate a priori ideas belong. It has a schematic status which alone is capable of abolishing the paradoxical element of duality. Descartes' critics think that by comparing the body to a machine and the mind to some kind of superior soul-substance he committed the philosophical error of admitting a duality between mind and matter. This charge altogether fails when we see that the absolute animal-spirit-substance is the common basis both of thought and extension which are the two main expressions of life referable to the two intersecting coordinates which have to be treated together as belonging to the same structurally conceived substance.
Coming now to questions more directly related to method, there is the notion of methodic doubt. Descartes recommends this for the correct guidance of human understanding in its search for truth and certitude in clear apodictic terms. This clarity is not necessarily experimental, yet it shares with science the spirit of scepticism which refuses to believe before sufficient clarity for belief has first been guaranteed by proper methods of investigation. Certitude according to Descartes lies within oneself. It is neither to be one-sidedly attributed to a posteriori thinking nor to the conceptual a priori side.
The understanding has to be guided properly along lines of maximum certitude, starting from the core of the total knowledge-situation which necessarily lies in human consciousness and not anywhere outside. The famous Cartesian dictum, cogito ergo sum (I think therefore I am) puts its finger on this central and neutral meeting point of all certitudes. Superficial critics have fallen into the error of treating this dictum as a compressed form of syllogism and some of them have tried to extract the converse of it so as to prove its absurdity. In whatever familiar logical form this dictum might be stated, it is meant merely to refer to the structural zero point of the knowledge-situation which any systematic philosophy must postulate if it is to follow some definitely conscious method. On the plus side of the vertical axis, cogitations lead us to factual ideas, and innate ideas constitute a kind of rearguard in consciousness. Adventitious ideas necessarily bring up the flanks and imply an element of strangeness and accident, lacking full reality.
Descartes believed in God as a guiding factor for his moral conscience but this belief did not exclude his correct scientific attitude which depended on the right to doubt one's thoughts when they were not sufficiently clear. He accepted, side by side with a God, the Aristotelian notion of an 'unmoved mover,' and his scepticism started with methodically graded doubts in order to guide his instinctive dispositions and save himself from the pitfalls of error.
He was thus a true believer and a sceptic at one and the same time. This made him a puzzle to the Roman Catholic Church authorities who suspected him of heresy even though he openly avowed his belief in Catholic doctrine. Although not condemned as a heretic there is still a touch of martyrdom involved in his fears of Papal persecution which lent itself to be thought of as being both for and against the Church authorities.
3. DIRECTING HUMAN UNDERSTANDING
Cartesian methodology consists of directing human understanding by intuition along what Descartes calls "right lines". How is it possible by instinct or intuition to attain a knowledge of discriminating between what is right and what is wrong? Here we have not only matters of logical judgment but also the entering into the picture of value appreciation. Morality involves an axiological certitude where the notion of God, the Good, the Ultimate Goal etc., are the final causes for guiding conduct. It is here that the conscience comes in, and a moderated conscience characterized by wholehearted affiliation to the Good through a passionate love of truth has to correctly help in guiding human understanding.
The general idea of Goodness, Truth, Reality or God must descend to confirm the ascending reasonings built up by methodic doubt, starting with the legitimate scepticism that we have already referred to. Thus there is an ascending and a descending dialectic moving on a vertical parameter among higher spiritual or lower moral values. Existence, subsistence and value blend and neutralize one another yielding that whole-hearted and passionate search for truth which is the motive for the right conduct or human understanding. Words like whole-heartedness and "passion for truth" are meant to underline the absolutist nature of the complete morality of Cartesian philosophy. While remaining a priori and conceptual and even schematic in his approach, Descartes has a fully scientific methodology in its demand for certitude at every stage of its progress. Adventitious self-evident ideas pertaining to the matrix of the absolute substance called animal spirit, are first to be reduced and referred to in pure unitive terms, bringing them under the purview of res cogitans by an ascending or a descending process of methodic doubt or possible degrees of value certitudes.
In the domain of res cogitans with its origin implied in the dictum cogito ergo sum Cartesian methodology reduces and constructs its speculative findings freely and methodically, complying always with the requirements of mathematics, logic and experience. The rightness or wrongness of a certain line of thought or action is determined always by the self-evident truth-quality given to the intuitive mind at every stage of the double dialectical process. There is an orthogonal principle involved and necessarily implied here in the correlates which intersect at right angles. A right angle is so because it is more "right" than any other angle. Human intelligence relies on this primary orthogonal justification even in measuring simple lengths and breadths of objects.
Descartes is aware of such a rightness given to intuition for the guidance of human understanding, not only within the limits of the visible sciences, but also for guidance in choosing between alternative courses of conduct and value appreciation. There is a subtle interdependence between perceptual and conceptual rightness.
We read the following in his "A Discourse on Method" (Part III Maxim II):
"My second maxim was to be as firm and resolute in my actions as I was able, and not to adhere less steadfastly to the most doubtful opinions, when once adopted, than if they had been highly certain; imitating in this the example of travelers who, when they have lost their way in a forest, ought not to wander from side to side, far less remain in one place, but proceed constantly towards the same side in as straight a line as possible, without changing their direction for slight reasons, although perhaps it might be chance alone which at first determined the selection; for in this way, if they do not exactly reach the point they desire, they will come at least in the end to some place that will probably be preferable to the middle of a forest. In the same way, since in action it frequently happens that no delay is permissible, it is very certain that, when it is not in our power to determine what is true, we ought to act according to what is most probable; and even although we should not remark a greater probability in one opinion than in another, we ought notwithstanding to choose one or the other, and afterwards consider it, in so far as it relates to practice, as no longer dubious, but manifestly true and certain, since the reason by which our choice has been determined is itself possessed of these qualities. This principle was sufficient thenceforward to rid me of all those repentings and pangs of remorse that usually disturb the consciences of such feeble and uncertain minds as, destitute of any clear and determinate principle of choice, allow themselves one day to adopt a course of action as the best, which they abandon the next, as the opposite." (4)
Put in common-sense language, the above maxim can be looked upon as tantamount to asking a person to follow the dictates of his conscience through his intuitive understanding. It is also capable of being understood in the light of Cartesian analytical geometry where a vertical parameter implies an orthogonal reference to possible horizontal errors of judgment. Doubt and indecision are great enemies to a whole-hearted pursuit of truth as understood in Cartesianism.
Absence of doubt does not necessarily mean belief in a hypostatic God, but rather combines with the scepticism that is its natural and necessary counterpart. Certitude thus is a point that moves up or down along the vertical parameter given to intuition. Even in cybernetics an orthogonal matrix is involved for the thinking machine to arrive at a stability of output having a maximum truth value. Thus the Cartesian method fully respects the logical structure that science is coming to recognize more and more in all precisely understood disciplines, hitherto divided and relegated into the distinct compartments of physics or metaphysics. It is now possible to treat them both as belonging to one and same integral structural context.
4. THE STATUS OF THE HORIZONTAL REFERENCE
After roughly understanding the implications of the vertical reference of res cogitans it is not impossible to recognize its own horizontal correlate. Here it is the attitude of the subject, when interested in outward objects, persons or personified ideas understood in the axiological context, which become correctly referable to this horizontal axis. The emotional states of man arise from his love or hatred of things. This results in happiness, suffering or morrow.
Descartes enumerates such states as passions and lists them as wonder, love hatred, desire, joy, and sorrow. There is a circulation of interest here beginning with wonder and ending with Sorrow.
This alternating process tends to repeat itself in a cyclic figure-of-eight, referable to the plus and minus sides of the horizontal correlate in pure self-evident conceptual and a priori terms and always having a schematic status. The methodology comes in when we understand the process as operating alternately in a necessary order of succession natural to normal man. Passions can be discarded when, by long repetitions of this alternating process, a point of surfeit or saturation has been attained by the person wholeheartedly seeking truth. In principle, however, the horizontal axis is never totally abolished as long as its use for guiding understanding is present.
The contemplative methodology in the context of a passionate search for absolute truth is seen to follow the broad lines of our structuralism. The essence of this methodology consists of a schematic reduction and verticalization of the self-evident factors involved under the overall categories of existence, subsistence and value. This essential feature is also adopted by Narayana Guru in this chapter. The negative movement of speculation started in this chapter is maintained up to the end of the Fifth Chapter. Thereafter what follows is not a reduction but a construction, still retaining however, its unitive and more positive tendency. In the last Chapter this tendency is finalized in the perfection of the man of nirvana.
5. A NEW WAY IN PHYSICS
We have just seen how Cartesianism implies the beginnings of a structuralism which affords us a means by which not only can time and space be treated as correlates, but also one which can act as an instrument of research extended into the whole range of philosophy. A total philosophy, structurally conceived, will include rationalist and even value-factors, ethics, and aesthetics. All can be discussed in a structurally unified and integrated fashion. The barriers that have kept physics and metaphysics apart can now be treated in a unitive fashion. Physics and metaphysics have been enabled now, by the common structure underlying both, to be treated as one and the same integrated whole in the context of a total truth.
The most epoch-making event that has taken place in our time is the formulation by Einstein of his Relativity theory. No other theory in modern times is so much talked about. Although Einstein took particular care not to erect a philosophy by characterizing the world of physics as a reality based on a sufficiently radical concept of relativity, still his theory has not failed to shock common sense.
Relativity as first formulated by Einstein within the scope of the Restricted Theory does not admit of any unique or universal Time which common sense tacitly assumes and which absolutist philosophy always presupposes. There are many frames of reference possible to a relativist and pluralism, as one of them, goes better with relativity than any unified notions of an absolutist nature.
The plurality of times is thus a corollary directly derivable from Relativity Theory. When the plurality of the reality of time is conceded philosophical pluralism is tacitly assumed. In spite of the care that Einstein took to keep his theory within the bounds of physics, we now find that it has become the fashion among modern thinkers to put pluralistic or relativistic notions on the pedestal as a sort of article of faith in order to uphold such a theory before the public eye in the name of progress, technocracy or civilization.
The spectacular triumphs in modern science have added their large volume of support to this technocratic attitude. As a result there is now a serious disruption of the sense of right values. It is therefore highly desirable that this lopsided approach to truth be rectified by a full formulation of the Science of the Absolute where both physics and metaphysics can coexist without conflict. The epoch-making step taken by Einstein in formulating his Theory of Relativity is not however a step taken in the wrong direction. On the other hand, Einstein started a new tradition in physics, implying a revised epistemology and methodology that no more emphasizes experiment and observation as unilaterally understood, but instead relies on the observer and the observed as correlated counterparts. The new physics relies more on mathematics than on mere observable laboratory experiments. It represents an attempt to bridge the gap between axiomatic and experimental thinking. The Cartesian correlates play an important part in relativity theory where they are treated as time and space belonging together to one and same continuum. Whatever the term "continuum" might mean, we enter here into a new kind of physics where time, that is not visible, and space, that is evident only through visible objects, are treated together as belonging to one and same knowledge-situation, whether that of physics or metaphysics. Thus physics and metaphysics come together and overlap in the post-Einsteinian version of the expanding or contracting universe with its red or violet shifts.
The more radical mathematical view of the universe of cosmologists like Kepler, Galileo and Copernicus has also been found inadequate by Einstein, although it is not very easy to determine at present where exactly we stand in respect of the physical world presented to us by modern physicists. One thing is certain however; that many conventional notions have been put into the melting pot. The physical world that we are now asked to accept for the common purpose of intelligently guiding human life is full of inconsistencies, improbabilities and impossibilities. The way out of this impasse consists, not in retracing our steps from the point to which relativity theory has taken us, but in going forward boldly to face the fullest implications and consequences of relativity. It goes without saying that relativity as a guiding characteristic of all physics must necessarily presuppose its opposite of absolutism so as to have any linguistic validity at all. Thus we are faced with the problem of putting relativity and absolutism together in the name of an integrated Science of the Absolute.
When one says that there are absolute and relative truths, one unconsciously creates in the mind two rival entities answering to the requirement of what is called truth. These two rival truths are two limiting instances of a more neutral and central notion which combines in its scope these two possible variations. Thus we have, in the context of the two antinomies referring to the absolute as plus or minus limiting notions, one which can be pluralistic and another which will not admit of any pluralism. What admits of pluralism can be placed subjectively, for purposes of linguistic clarity, at the bottom of the vertical axis. What does not admit of pluralism as a concept more positively understood finds its place as a limiting case on the plus side of the vertical axis. The normative Absolute will have its structural position at the very centre of the total knowledge-situation. This means we have a relative of an absolutist context and an Absolute of an absolutist context. They are positive and negative limiting cases of a normative Absolute which implies normalizing with reference to the two others.
Such are some of the semantic and epistemological implications which we have to keep in mind in. order to avoid confusion in the matter of understanding all things sub specie aeternitatis.
The methodology and structuralism tacitly presupposed in the Darsana Mala imply both a reduction and a construction by which multiplicity is first reduced to negative unity in the first five chapters. Both plurality and duality get abolished by a method of elimination of what is doubtful and unessential.
Having touched the rock bottom of ontology by this negative reduction, the last five chapters aim at a more positive construction, implying the normalizing of existence with its own rational subsistence. There is a construction implied in the method here by which ontology gets transformed into a value world where teleological first and final causes gain gradual primacy. Even at this stage of reconstruction there are always the Self and the non-Self involved as irreducible counterparts related by complementarity, reciprocity and cancellability. We shall explain these later on. Here we have only to remember that the methodology of this work has to be treated together with its own epistemology and axiology.
The methods of mathematics and the rules of logistics or semiotics could be looked upon as operating from one limb of an equation, and the resultant understanding could mean the same truth seen from opposite sides of a total knowledge-situation. These methods and rules are not outside the world of discourse proper to an integrated Science of the Absolute. They have to be thought of as legitimate features of the methodology which we are here concerned with. Pluralism might be admissible in a merely utilitarian philosophy. Axiomatic certitudes of mere idealism might support only one Truth. The modern scientific tendency which gives to percepts and perceivable realities a place more important than concepts and conceivable realities takes a one-sided position. It goes without saying that such preference for the perceived is a partiality of the scientist which cannot be admitted in a normalized integrated Science of the Absolute, where all realities are to be viewed in an impartial and neutral light. No philosopher should have any "private axe to grind" as Bertrand Russell rightly asserts. Bergson puts the same requirement in better form when he says he proposes to follow the rule as one "of not accepting anything which cannot be accepted by any philosopher or scientist, nor accept anything that is not already implied in all philosophy and science". (D & S, pp.87-88).
Even Eddington revised scientific epistemology for his Philosophy of science, as we have already pointed out. He wants to give concepts a more important place than scientists have hitherto given them. He takes his position as a non-experimentalist and categorically asserts that it is concepts that matter.
Concepts and percepts belong to the same total knowledge-situation when they are accommodated under one and the same schema. Bergson does not find any objection to such an inclusion of conceptual and perceptual factors, and says: "they could be represented by the same schema". (D & S, p.84)
We also read the following from Bergson:
"I can also conceive that all the points of the universe that are mathematically related to the present and to the past - that is to say, the future unraveling of the inorganic world can be represented by the same schema." (D & S, p.84)
We have here to remember that the actual time that passes has a perceptual status and future time has a conceptual or metaphysical one. Our inclusion of both these aspects in one and the same schema is justified by thinkers like Bergson, who have improved on the schematismus of Kant on lines we have already explained. The two correlates schematically referring to the time and space of Einstein, the res cogitans and res extensa of Descartes, and the natura naturans and natura naturata of Spinoza can all be fitted into one schema.
We can even extend the application of these same correlates into the domain of Vedantic thought where reference to the horizontal as the world of effects and to the vertical as the world of causes is found. In the language of the Bhagavad Gita one can think of the same correlates as representing the field (kshetra) and the knower of the field (kshetrajna). The latter is the vertical because of its attenuated or refined status, referring to the same universe of Einstein wherein the observer and the observed have to belong together to a context common to the liquidity of matter and the fluidity of mind.
Newtonian physics is a limiting instance of modern post- Einsteinian Physics which insists on characterizing itself in its own deliberate way as relativistic in outlook.
Absolutism thus implies relativism and it is by giving to these terms their proper places in a normalized schematic totality that ambiguities and confusions can be avoided. Such a schema is what we have suggested all along.
In this present chapter it will be seen that Narayana Guru relates the world of effects to the world of causes. This implies a negative reduction of horizontal factors into vertical terms. This gives a mathematical or dialectical reduction of counterparts wherein the visible world is absorbed by gradual steps through reasoning into its existential or ontological residue of absolute reality. Even when reduced in terms of existence it continues to be characterized by subsistence. Its rationalist status and value belong to the world of aesthetic or ethical significance pertaining to axiology. Finally characterized by existence, subsistence and value, this Absolute as seen from a total philosophical or scientific standpoint. We have thus to first arrive at the ontological Absolute by the method of reduction. A positive mathematical construction would then yield place to this negative methodic reduction. The present Chapter is meant to explain in broad outline the implications of this negative methodology.
6. RELATIVE AND ABSOLUTE TIME
Common sense takes it for granted that there is a unique and universal time having its reality in the minds of animals and man. Whether this duration is precisely measurable with the help of clocks or only understood in reference to sunrise, sunset etc. such a common experience of time is a matter that is not usually put into question. Even in such matters vouched for by common sense there is a possibility at present of two rival positions between sceptics and believers.
Modern scientists or empirical and positivist philosophers prefer to call themselves sceptics who have no use for any unique or universal notion of time. Such a time according to them would have an absolutist status. Because relativism and pluralism are now in fashion, in the name of a scientific tendency treating all metaphysics as nonsense and excluding belief in any God or even in a godlike entity, it is only to be expected that the relativistic outlook does not tolerate the unique time of common sense. Relativity puts the observer and the observed together at various points of universal space and every observer relates himself to the observed belonging to his particular pluralistic frame of reference. Time is thus measured preferably in piecemeal fashion rather than in any wholesale manner by relativists. Relativity results from the interaction of many possible observers placed at various points in space, each with a corresponding event in the universe he is observing , with or without the help of instruments.
When the counterparts of the observer and the observed are brought into interrelation, participation or interaction, the resulting relativist universe does not admit of one time but only of a time that is multiple. Light being independent of both space and time and of any movement of its source can, in principle, yield simultaneity and not duration.
Even such a natural position is not presupposed, at least by the "restricted" theory of Relativity. It is easy to see how this theory recognizes and gives primacy to spatialized factors, referring to the horizontal axis, in the structure of the Absolute.
In the General Theory of Relativity time and space enter together to be treated as a continuum. Here we begin to have the vertical correlate representing time coming into the picture side by side with space. The fragmented time implied in the Restricted Theory of Relativity is one that has shocked both common sense and ruled out the philosophers´ belief in absolute time. Sceptical philosophers favour this kind of time as against the absolutist a priori time which metaphysicians glorify sometimes, putting it on a pedestal and giving it equal footing with a theological God. Descartes could be cited as representing such a philosopher who speaks of pure duration as given to intuition as a divine factor. He did this in order that his occasionalism could operate.
Time could either be related to mechanistic or to creative evolution, and there are philosophers like Julian Huxley who admit time into their metaphysics, yet claim to remain empirical scientists. There are, however, various brands of evolutionism, some mechanistically biased and others conceived on a more fluid basis and called 'creative.' To the extent that time is included as a pure duration given to intuition, strict scepticism may be said to yield place to some sort of belief.
Between scepticism and belief history has produced many instances of martyrs who have suffered the highest penalty for believing truths unacceptable to orthodoxy. Even Descartes had to withdraw his book on cosmology which was being printed at the time when Galileo was being condemned for heresy. Bruno was executed for not believing what the authorities wanted him to believe about the universe. Some of those who first suffered because of the Church have later become acceptable and some, like St. Joan, have even been canonized. A Science of the Absolute has to recognize both kinds of martyrdom with equal fear or favour as the case may be. It cannot take sides. The same applies to the question of accepting or rejecting the claims of a unique or universal time.
This means that the Science of the Absolute cannot altogether refuse to give due importance to the practical reality of time or duration. To do so would be to take the side of those who deliberately wish to do violence to common sense. The question of duration which is so directly within the scope of human experience can be scientific even when we decide to take the side of believers as against sceptics. It is a neutral and normalized position that is proper to any correct Science of the Absolute. In the light of the prevailing vogue in the scientific world of not recognizing universal time or the duration that presupposes it, what is the position that we should take? Is there a correct scientific methodology whereby we can arrive at a unique and universal time while starting from the relativistic position in respect of time implied in the limited theory of Relativity?
Does such a methodology take account of the modern scientific equations and experiments? It is these alone which give strict scientific status to the reasonings and calculations of this new methodology required to admit a unique and universal time on a par with its own relativistic counterpart belonging to the same total knowledge-situation? If they are put together under the same schema combining physics and metaphysics are we able to attribute a homogeneous epistemological status to both of them together? What is the nature of this neutral monistic substance or stuff in which time and space exist without contradiction, participating in matter and mind at one and the same time? Does this neutral substance resemble the animal spirit of Descartes or does it rather answer to the structure of non-Euclidean geometry where, losing its radical rigidity of uniform motion in straight lines as in classical physics, this neutral stuff accommodates the notion of a space-time continuum. When treated as neither mind nor matter , irrespective of the observer or the thing observed, do we not attain to the position of postulating what Narayana Guru in this chapter calls chaitanya, or vital consciousness?
Such are some of the questions that we might be called upon to answer when we are concerned with a methodology for the Science of the Absolute. In the present chapter moreover we are concerned with effecting a transition from the world seen as an effect or a presentiment, to one where causes and effects can be treated together on a more neutral and homogeneous ground.
A Science of the Absolute cannot tolerate an inner tautology or an outer contradiction. Besides methodology, as we have already said, such a science must have its own epistemological and axiological presuppositions or implications consistently belonging to it. We have to avoid at any cost being merely conventional in such matters, whether in the name of traditionalism or of progress. When we keep all these questions together in our mind it will be seen that there is hardly any literature available at present which takes the correct impartial position between the two disciplines of physics and metaphysics. Starting from what is known through the senses and thus naturally with realities that depend on space, we can travel step by step to attain a notion of pure time that is not directly given to the senses. Thus we have to travel from rigid objects in space to the pure flux presupposed by absolute time. The limiting instances in such a journey that we can understand mentally are precisely those of classical and modern physics. The steps of such a transition from a rigid or radical universe to a universe that is recognized as affiné or refined, together with a notion of time proper to each of them, have been worked out in great detail, without omitting any experimental or mathematical details, by Henri Bergson in his Durée et Simultanéite.
Strangely enough, Bergson withdrew this work in the year 1922, Even though he pleaded for a time that is given to the common sense of all men irrespective of scepticism or belief, Bergson had to be cautious and circumspect. It was not however in the name of the prevailing values of any orthodox religion, but strangely in the name of scientific scepticism that he acted. Concerned as we are with the methodology proper to the reduction of the relativistic or horizontal multiplicity of pluralistic factors or elements into unitive terms, we are also interested in supporting our arguments fully with experimental and mathematical notions of modern science. Bergson's work comes admirably to our rescue here. We cannot enter into minute examination of all the implications found in Bergson's suppressed work, but we will rather only concern ourselves with those parts of the book which directly support our own arguments. Bergson says he wrote the book for the following reasons:
"We have undertaken this work exclusively for ourselves. We wish to know to what extent our conception of duration was compatible with Einstein's view on time." (D & S, p.v)
Bergson was also interested in Einstein because, according to Einstein's way of thinking, "science and philosophy are different disciplines but are made so as to complete each other." (D & S,p.v). Thirdly, Bergson considers that there is a paradox that spoils the clarity of time as understood by Relativity. He explains its nature as follows:
"We have had to call special attention to the paradox of the theory of Relativity, to the multiple Times which flow with greater or lesser speed, and to the simultaneity which could become succession and the succession which could become simultaneity when one changed the point of view".(D & S, p.v)
"The general theory of Relativity comes to place itself on the side of time when it wishes that one of its coordinates would effectively represent it." (D & S, p.viii)
These three features can be understood with their various implications only when we keep in mind the questions we have suggested above (pp.298-299). It will be further helpful for the reader to begin to think in terms of the schematic language that we have developed, in order to follow more easily those preliminary remarks of Bergson. Let us also say here in advance that we shall hereafter take the liberty of relying more and more on the structural language of our protolinguism. If such a linguistic device proves in any way helpful to the reader, that itself would amount to its justification and add to its validity because of the useful purpose it serves.
7. BERGSON´S FIVE OBJECTIONS TO RELATIVITY
Bergson is interested in making philosophy a discipline that can be treated with physics in order that both physics and metaphysics could form one integrated or unified discipline. This can be called a science or a philosophy as one prefers. What results is a philosophy of science or a science of philosophy, or even a science of sciences. In our view this is no other than a Science of the Absolute.
In India, brahma vidya is referred to as the science (vidya) which is the foundation of all sciences (vidyas). It deals not merely with "truth" but with the Truth of truths, the light of lights, or the Value of all values. The Absolute is the natural and normative notion around which this science was built. When stated in such a wholesale fashion the Science of the Absolute becomes repugnant to the spirit of modernism because it appears as a seemingly totalitarian discipline. Totalitarianism in politics and religion has left a bad taste in the mouth of most Europeans, who prefer a humbler piecemeal approach to truth. In spite of such an understandable objection, this is in itself another form of prejudice not necessarily justified with equal force in other contexts, outside religion or politics.
Bergson's hesitation to characterize his attempt to give time its legitimate importance and place in a more broadly conceived science than hitherto, is thus quite understandable. He has said openly in his Preface that he was interested in seeing how far the time of common sense corresponded to the time of Relativity. Each observer of a given system has his own time reference independent of his rival in another system. Such was the basic presupposition of Relativity, legitimate only in the context of physics as a discipline distinct from metaphysics. This kind of time shook commonsense as well as the philosophical notion of a unique and universal time that metaphysics always assumed.
Bergson is interested in showing that there should be a time that could be viewed as both perceptually and conceptually valid with equal force. In taking a central normalized position in respect of time, Bergson is in reality arguing the case for a Science of the Absolute. The time that interests Bergson is therefore a fully normalized version of absolute Reality, perceivable, and conceivable at one and the same time. He fits such a time into a common schema that is independent of relativistic physics and pluralistic philosophy.
It is therefore not wrong to assume that the unique and universal Time that Bergson is interested in is no other then the absolutist version of the pluralistic time of Relativity. We have already said that it is possible for the purposes of this Science of the Absolute to choose any one of the basic categories that find place in the totality of the structure of the Absolute so as to revise and restate its status and give it a neutral, central or normalized position for the clarification of the content of the Absolute.
In this chapter Narayana Guru refers to the notion of cause rather than of time. Whether cause or time is used, for our purposes of clarifying methodological aspects here, the resulting steps of the argument involving the reduction that we have spoken of remain unaffected. It is therefore no less useful for us to follow the steps of the scientific reasonings of Bergson, even when we should be thinking of cause and effect rather than universal and unique Time. The first and final material cause of the universe must have an absolutist status in the same way as the multiple time of Einstein must presuppose more philosophically an absolutist concept of Time. It is in this light that it is interesting for us to pay some attention to the five main objections of Bergson to the pluralistic time of Einstein.
8. BERGSON´S OBJECTIONS EXAMINED
Bergson's five objections are as follows:
"It is because of not having defined with rigour the terms employed, it is because of not having been sufficiently habituated to see in relativity a reciprocity, it is for not having had constantly present before the mind the relation between radical relativity and attenuated relativity, for not having been cautioned against a confusion between the two, and finally for not having pressed sufficiently together the passage from physics to mathematics that one so seriously erred on the philosophical meaning of the considerations of time in the theory of Relativity." (D & S, p.52)
Even before formulating these charges so boldly and categorically, Bergson explains in the Preface that a major paradox is hiding at the core of the problem and is responsible for all these errors. In our own words we can say that this paradox consists of whether one should take a horizontalized and spatial view of the universe or a verticalized and temporal one.
In Bergson's own words:
"The confusion of this basic paradox is in the mind of those who erected this physics as such into a philosophy. Two different conceptions of Relativity, one that was abstracted and the other imaged, one that was incomplete and the other achieved, coexisted in their minds and interfered with each other. In dispelling this confusion one made the paradox fall."
(D & S, p.vii)
The task of making the paradox fall as Bergson proposed to do is tantamount to the task of abolishing relativism altogether along with its implied pluralism. Whether such pluralism implies time, space or both, it is nonetheless understood that a non-pluralistic notion of the Absolute should be attained. Bergson as a philosopher who denounces conceptual or conventional metaphysics cannot be expected to say this as openly as we do here. An examination of his laborious work is sufficiently convincing on this point all the same.
A process of becoming or flux understood in terms of life is the ultimate absolute reality for Bergson.. In the present work, as in all his other works, he seeks to find support for this flux of the élan vital at the basis of creative evolution. Spatialized time is converted and understood in terms of a time that correctly represents this unique and universal Time for which Bergson's philosophy stands. The duality of time and space found in the Cartesian analysis of absolute substance is abolished by Bergson. He does this in terms of a dynamism that is ever in the process of a creative becoming. He however takes care to present a schéma moteur more dynamically conceived and without a Cartesian fixed frame of reference. The logical and semantic purpose or use of correlates is not discarded by Bergson. If we keep these features of Bergsonianism in mind it will be easier for us to follow clearly his own line of attack on relativity theory.
Bergson's main task is to give a unique and universal status to time by ridding it of its spatialized and pluralistic prejudices. In order to accomplish this difficult task he makes use of the same mathematical equations which Einstein used. The contraction of Lorentz supported by Fitzgerald depends upon a mathematical transformation taking place between the terms of an equation. We know elsewhere from analytical geometry that equations can answer to lines on a graph and vice versa. There is a rigour, adequacy and a possible homomorphism to be presupposed between them. The two proofs of the Pythagorean theorem refer to the same central truth which can be looked upon in a formalized and logical, or a structural and geometrical fashion. They belong together to one and the same mathematical entity.
The Lorentz equations answer to the correlates or vice-versa. Both obey the same relational laws in nature, logic and the propositional calculus. Schematism can be treated either protolinguistically or metalinguistically.
We have explained these possibilities at length elsewhere. Bergson in following up his revaluation and restatement of the relativity theory without its paradox, next turns to the equations of Lorentz. When schematically understood they reveal the same structural pattern based on the reciprocity between timelike and spacelike factors in the physical universe which are both gross and subtle at once. The Lorentz equations apply to an attenuated and refined universe wherein contractions and expansions involve distances to be expressed by six decimal points, observable only indirectly through red and violet shifts or by the aid of a tentative mathematics based on a priori postulates and axioms. Strictly speaking these postulates and axioms have only a hypothetical and non-experimental status of their own. The validity of some of the remaining assumptions are left to be fully verified by future observations of the micro- and macrocosms.
Bergson however is on safe ground when he bases his objections on the very same equations that Einstein used in his theory of Relativity. In his work under reference here Bergson has used the same mathematics as Einstein and also the same frame of reference implied in the Michelson-Morley experiment. Light affords an absolute frame of reference and the failure of the Michelson-Morley experiment to show any fringe effect further proves the fixed, immobile and absolutist status of the space in which no ponderable ether in motion is found.
Both the equations of Lorentz and the observations made by modern physicists have, in the structure of space in terms of the velocity of light, an absolute frame of reference. Newtonian space and motion have a rigid status and are considered absolute by Einstein in the sense that they are treated as independent of the observer. Classical physics is not however altogether dispensed with by Einstein. It is often referred to as a limiting case for the world in which the relativity theory operates. We cannot enter into all these implications of absolutism or of relativism that enhance or detract from the value of the relativity theory. It is therefore safer for our purposes to follow the same line of reasoning as Bergson.
By doing so, as he says, the case for a unique and universal Time still remains valid and fully justified even according to the mathematical equations of modern physics.
"To know this (that is to know what interests the philosophers rather than the physicist) we have taken the formula of Lorentz term by term and have searched for the concrete reality and the thing perceived or perceptible that each term corresponded to. This examination has given us an unexpected result. Not only did these arguments not contradict themselves, they also confirmed and accompanied the commencement of the proof of the natural belief of all men in respect of a Time that is unique and universal." (D & S, P.vi)
Bergson here is evidently interested in giving to time a universal and unique absolutist status. We have to remember in following his methodology that the same can be applied in an extrapolated manner to the question of a unique and universal principle of causation. The change from Time to Cause would change nothing in the methodology. It will only be an additional case where the Absolute would become once again reaffirmed.
9. BERGSON´S FIRST OBJECTION
In the enumeration of his five objections against relativity theory, Bergson puts the first one as, "not having defined with rigour the terms employed." In the first two chapters of his work he uses terms such as "demi-Relativity" and "unilateral Relativity". He also refers to reciprocity as a more suitable term than what he refers to as "incomplete Relativity". He also uses the phrase "complete Relativity" for his revised version. It is important to see how far he is justified in thus revising or applying his correction to the Theory of Relativity as presented by Einstein.
Einstein speaks in the name of physics and he is perfectly correct in doing so. Bergson on the other hand as a scientific, philosopher is speaking in the name of a unique and universal Time of common sense, free from the mere world of particular physical distances and events mechanistically understood in multiple time.
We are not merely interested in such a philosophical view of Time as a flux with an absolute Reality, but in the larger context where duration and distance are both included within an absolute principle of causality. We have elsewhere made some general remarks about such matters in order to clarify our position (see p.916 below).
In taking up one by one the five objections raised by Bergson, we are making an effort here to clarify the position afresh. Scientific truths can be stated in simplified fashion so that men of commonsense will feel their rightness even when they have no technical training. We are not against any notion that resembles the Absolute . We keep an open mind in this matter and understand why modern science finds it repugnant to think in terms of one absolute truth and avoids anything resembling the a priori approach. We have already explained elsewhere the origin of such prejudices which cannot be continued into our own attitude in respect of an integrated Science of the Absolute. Let us now try to restate the position of physics and Bergson's approach.
The Michelson-Morley experiment has given Physics a mathematical and structural frame of reference involving the Cartesian correlates and the equations of Lorentz. A new way in physics was thus opened up by Einstein. In this new physics the observer and the observed belong to the same spatio-temporal frame of reference. Distances in space are more easily perceivable than intervals in pure Time. Relativity must refer to both Time and Space as belonging to the same homogeneous matrix or basis. To make them belong together thus was a philosopher's task rather than that of a physicist.
Thus, when the Michelson-Morley experiment failed, the average undaunted physicist started to theorize about space-time relations within his own arbitrarily postulated closed systems where a physicist observer interested in perceivable realities was supposed to live within what he was observing. This was at first crudely accomplished either with mechanical clocks or by the measurable distances of the moving system. Refinements were introduced stage by stage resulting in the "restricted", "general" and "unified" views of Einstein. Such is the basis of the relativity theory erected by Einstein as a revaluation of Euclid and Newton. The ensuing convulsions and sensations in the world of general philosophical thought rudely shook all previously held notions about the physical universe. It was at last given to Bergson to bring forth his arguments in order to salvage at least the case for a unique and universal Time.
The denunciation of absolutism seemed to gain some unduly exaggerated initial momentum at the time when Bergson thought fit to intervene to save Time from the permanent damage of being forever discredited. His arguments seen in this light more clearly reveal their validity and force.
We are concerned here specially with his first objection which is that of not defining the terms with rigour. He means that the term "relativity" as used by Einstein only amounts to a demi-Relativity or an incomplete or unilateral Relativity. In justifying this charge Bergson points out certain innate inconsistencies presupposed especially by the restricted theory of Relativity where Space rather than Time is treated as more important. The familiar example that is given when one tries to explain the implications of this theory is that of a train moving at a speed approximating the speed of light. It moves in a direction that is horizontal and at right angles to a fixed source of light placed somewhere to serve as a reference. The length of such a train when travelling in the direction of light is supposed to shrink into nothingness when the speed corresponds to the velocity of light. Such is the theoretical assumption of the Lorentzian equation, implying a Fitzgerald contraction in the context proper at least to the Restricted Theory of Relativity.
If the common man should ask such a relativist whether this contraction is observed or observable he would say that such observation is only possible if the observer could be placed within an immobile and independent frame of reference. The possibility of such a perceivability in science together with the theoretical conventions proper to it is the basis of the validity of the contraction. These conventions are accepted only to the extent necessary to justify the truth of relativity as a physical and not a metaphysical reality.
The assumption of the physicist is that even though the Michelson-Morley experiment failed, the actual physical medium in which space and time are to be interrelated through velocities and intervals such as that of the motion of the earth around the sun, is still within the scope of a possible perceivable calculability. This is accomplished by the cooperation of postulates, axioms and conventions in modern mathematics on the one side, and on the other side by possible recorded observations or verifications. Many of the implications of the three tentative theories are still to be verified.
Such is the thin, attenuated and highly refined world situated at the point where rigid realities are made to melt and blend with a world to which the red shift legitimately belongs. The status of such a universe is at present exceedingly vague and questionable, even in the eyes of strictly trained physicists.
Is it any wonder that the philosophical instinct is rudely offended by some of the easy assumptions of prevailing relativistic thought?
We do not feel competent to enter into the merits of this discussion which requires a more mathematically trained mind. Also we do not wish to part company, if we can at all help it, with the claims of physicists when they are found valid from the standpoint of a future Unified Philosophy of Science. We shall therefore rely on some direct quotations from Bergson to show how, without violating the requirements of a scientific methodology still based on acceptable mathematical conceptions of our time, he is able to reveal to us some of the errors and anomalies of relativity theory. The following quotation is from Bergson's first chapter, entitled "Demi-Relativity":
"We wish to manipulate all the transitions between the psychological and physical standpoints, and between the Time of commonsense and the Time of Einstein. For this we have to place ourselves in that state of mind where we one can find oneself at the original point when one believed in an immobile ether in absolute repose, while at the same time explain the Michelson-Morley experiment. We shall thus obtain a certain conception of Time which is half relativist by one side only and which is not yet that of Einstein, but which we think is essential for us to know. The theory of Relativity may not take any notice of it in its deductions which are scientific in their proper sense: we believe it is subjected all the same to its influence as long as it stops short of being a physics that wants to become a philosophy. The paradox that frightened some and reduced others so much, seems to us to come from this. It depends upon an equivocation. It is born from the fact that two representations of Relativity, one that is radical and conceptual and the other that is attenuated and imaged, accompany each other in our unconscious mind arising from the fact that the concept is subject to the contamination of the image." (D & S,pp.2-3)
On examination the above paragraph brings into relation two aspects of absolute Reality which Bergson has distinguished clearly. He has elsewhere tried to apply other predicative attributes to it. In doing this, Absolute Reality becomes a paradox both to the physical theorist and to the scientific philosopher.
In our structural language it is fully legitimate to refer to these aspects as the verticalized and horizontalized versions of the same absolute Reality which can be attained when the implicit paradox is dissolved. Bergson also clearly recognizes this.
Newtonian physics with its laws of motion is the horizontal version of spatialized reality, while time treated as a continuum with space as found in Einstein's General Theory is the vertical correlate belonging to the same paradoxical content. It is in this sense that Bergson, in the concluding sentence of his work, sums up the position of Einstein when he says that "Einstein is the continuator of Descartes." (D & S, p.241)
Descartes' two categories of res cogitans and res extensa correspond to his correlates. These correlates represent by their intersection space-like and time-like aspects of absolute substance and the principle of universal causality can also be located at the point of origin of the four-limbed quaternian structure. These are matters we have already elaborated sufficiently in their logical, semantical, structural and schematic implications. A logarithmic curvature of space and time can find its place at the same point in the vertical axis. We have already quoted (see pp.154-155 above) more than once from Bergson's "Durée et Simultanéite" where he graphically elaborates the structural implications of a complete theory of Relativity. As a result of all these discussion carried on term by term and stage by stage, Bergson is able to give to Time a unique and absolutist status.
There are two footnotes in Bergson's work which are of special interest to us, and since we are still concerned with demi-Relativity we shall quote them. The first footnote refers to the common sense question which is concerned with the contraction of the length of a body when it moves in the direction of light. The question can be asked, "What happens to the height or the breadth of a body, if any, which cannot shrink because of being at right angles to the direction of the propagation of light?" This objection is referred to by Bergson as follows:
"It seems, in the first place, that instead of a longitudinal contraction one could as well have supposed a transversal dilation, or one or other at one and the same time, in the correct proportions. On this point, as on many others we are obliged to leave aside the explanations given by the theory of Relativity. We limit ourselves to what interests our present research."
(D & S, p.8)
Such incompatibilities arise from the violation of the basic laws of epistemology and methodology necessarily implied in mathematical equations and their corresponding visualized or structural versions, between which modern structuralists postulate a homomorphism. We shall now pass on to some other aspects of Relativity that reveal the incompleteness of the theory as pointed out by Bergson. In his second interesting footnote we read the following:
"It is important in effect to remark (one has often omitted to do this) that it is not enough that we take the contraction of Lorentz for establishing the point of view of the ether, the complete theory derived from the Michelson-Morley experiment performed on the surface of the earth. One has to join to it the lengthening of Time and the dislocation of simultaneity, all of which we shall come back to presently, after transposing them into the theory of Einstein. The point has been put into proper light in an interesting article of C.D. Broad called "Euclid, Newton and Einstein" (Hibbert Journal, April 1920)"
(D & S, pp.9-10)
It is evident from the above remarks that many aspects of relativity remain to be revised and completed in the light of a unified methodology and epistemology. Bergson takes the trouble of following up the broad assumptions on which the theory of Relativity is based so as to bring in, stage by stage, the corrections needed in the equations and the applied visible aspect belonging to the form of the equations. Here Bergson may be said to anticipate modern structuralists who see a common structure implied in all the laws of physics. When properly formalized or schematized they reveal a common homomorphism. At the time when Bergson wrote this the structural interpretation of the laws of physical nature had not yet become as acceptable or nearly accepted as it is at present.
Bergson is next seen to manipulate the Lorentzian equations conforming to the same axioms and conventions acceptable to the mathematicians of his time. In doing so he adopts the device of speaking of different time-space systems or schematized versions which represent the results of the Lorentz equations when applied to situations real or imaginary.
The first reference to such a rival system is to be found in the following quotation which is self explanatory. Moreover to speak of a proper frame or system of reference belonging to each observing physicist is not inconsistent with the overall position acceptable to the theory of Relativity. We read the following:
"Generally speaking, let us call S an immobile system and S' another sample of the same system, as its double, which in the beginning was one with it and which detached itself afterwards in a straight line and with a speed V. As soon as it departed S' contracts in the direction of its movement. All that is not perpendicular to the direction of the movement participates in the contraction. If S had been a sphere, S' would have the form of an ellipse. By this contraction the Michelson-Morley experiment is shown to give the same result as when light had a constant velocity and equal to C in all directions."
(D & S, p.8)
We are here concerned with three different aspects of reality. The first belongs to the immobile ether where the Michelson- Morley experiment reveals the velocity of light to be a constant. In the second we have a system S wherein an imaginary physicist named Peter is situated before any motion effects a contraction of space. Finally there is a system S' which is a double of the system S, subject to the contractions and dilations directly derivable from the Lorentzian equations. System S´ is occupied by an imaginary physicist, Paul. Both Peter and Paul have mechanistic clocks to refer to in each of their systems. When the implications of the equations are fully manipulated we get a more complete picture of Relativity than envisaged by Einstein. The manipulation of the equations and the visible implications of the same, (i.e. the mathematical and physical versions), are brought together by Bergson in the following way:
"In brief, the system S´ envisaged in Space and Time is a double of the system of S which is contracted in respect of space in the direction of its movement, which has dilated in respect of time in each one of its seconds, and which finally in time has dislocated in terms of succession all simultaneity between two events of which the distance is retracted in terms of space. But these changes escape the observer who is part of the mobile system. Only the fixed observer can see it."
(D & S, pp.20-21)
The incompleteness of the approach of Einstein is here initially exposed.
10. BERGSON´S SECOND OBJECTION
Bergson's second objection arises because "of not having been sufficiently habituated to see in Relativity a reciprocity." He points out that the term "Relativity" only means a unilateral and incomplete demi-Relativity. This is because the full implications of the equations of Lorentz have not been taken into account by Relativity theory. Bergson passes on in the second chapter to a closer examination of what he calls "Complete Relativity". His objection is more positive in so far as instead of merely correcting definitions and revising the terms of the equations, he rather proposes an alternative theory of his own. This theory is strictly based on the same equations and theoretical intentions of Einstein.
According to Bergson, relativity of movement implies a reciprocity when we think in terms of the distance between two points in the universe increasing or decreasing. One has no right to prefer to this two-sided standpoint a relation to motion which is taken only from any one of the points, because of the unilateral view of the distance involved. When we take a bilateral view we come closer to a complete theory of Relativity. Even Einstein as a physicist who is interested in measurements only because his theory claims to abolish the classical theory of physics and replace it with something applicable to the whole of the physical universe should, as Bergson thinks, agree to this. As soon as reciprocity is admitted by the physicist as the only legitimate point of view to take he will move from demi-Relativity to a complete Relativity theory. Ultimately he must do this because he already adopts and uses an axiomatic method when he manipulates mathematical equations.
Physicists who are content to verify their theories occasionally when some astronomical event or spectral shift is observed may not be interested in stating the theory in its correct and complete form. The practical laboratory physicist is content to travel from one working hypothesis to another. But a philosopher is interested in the status of Time in the theory of Relativity and his method is not limited to the experimental method. Bergson too fixed his vision. on visible and perceptual aspects of reality, as he is first a pragmatist and operationalist philosopher. It is possible for him to guide his own speculations along mathematically valid lines. This is exactly what he does when he boldly proceeds in his second chapter not only to reveal the position of radical Relativity known to Copernicus, Kepler, Galileo, and others, but also to reveal what he calls "Attenuated Relativity".
For the Newtonian scientist it was natural to think in terms of straight lines from some point of origin ending at some other point in infinite space. An outside force was needed to change the course of this straight line. Such a classical universe presupposed a Euclidean structure of space. Einstein's Theory of Relativity put these classical or radical features into the melting pot and boldly started a new way in physics. Bergson's complaint now is that, even having discarded classical physics, the new way has not been completely or consistently developed. Interested as he is in the status of absolute Time given both to philosophy and common sense, he also refers to the question of absolute movement and puts the relative movement already envisaged by the classical astronomers side by side with absolute movement which is no other than the verticalized version of relative movement in practical horizontal space. Pure or absolute movement belongs to the context of an attenuated theory of the universe and is more timelike than spacelike. This is because of its a priori mathematical character. Thus we have two limiting cases to keep in mind when we try to follow closely and intelligently the arguments advanced. This builds up into a surprisingly realistic picture of a colourful universe as contained in pages 42-52 of Bergson´s work and which we have quoted previously. (see p.148-153 above).
It will be easier for the reader to familiarize himself with this completed version of Relativity as understood in the light of Bergsonian philosophy before trying to follow further the system S and S' into which he has been able to reduce the implications of relativity theory at the end of his first chapter. These independent and closed systems, each with a frame of reference of its own, need not be thought of as big or small. Furthermore, they are independent of each other and interchangeable in status, although still belonging to the world of observing physicists who can look at their own systems without inconvenience or contradiction Each closed system is not unlike a monad of Leibniz, and does not preclude the thought of a system of systems like a Monad of monads.
Keeping these remarks in mind, let us now proceed to examine a few selected passages from Bergson. The first one refers to reciprocity as against demi-relativity.
We read the following:
"The 'Reciprocity' of movement is therefore a fact of observation .... science refers to measurement and measurement applies to lengths, and when a length grows or decreases there is no reason to treat one extremity as privileged: all that can be asserted is that the gap becomes greater or diminishes between the two."
(D & S, pp 36-37)
"Thus the relation between the two systems already mentioned as doubles of each other is treated as reciprocal. Reciprocity also implies a subtle philosophical aspect which was first outlined by Descartes where internal (felt) and external (measured) reciprocities are brought together into the same picture."
(D & S, p.37)
Further alluding to such a reciprocity, Bergson continues:
"Certainly it should be that all movements could be reduced in such a way as to be capable of being perceived in space. By the side of the movement that we can observe only from outside, there are those that we can also feel internally, as being produced. When Descartes spoke of the reciprocity of movement, it was not without reason that Morus replied: 'If I should be seated quietly and another on going away a thousand paces from me, should be red with fatigue, it is I who have been resting."
(D & S, p.37)
Here Bergson explains how it is possible for one or the other person involved in the situation described by Morus to decide to move, when we could even say that the ground moves away from the man or the man moves away from the ground. Animals and non-metaphysically minded men might treat the movement as unilateral. Movement thought of in itself has an absolutist character about which Bergson says later:
"He (i.e. the metaphysician) should penetrate into the interior of things, and the time essence, the profound reality of movement could never be better revealed to him than when he accomplishes the movement himself, even when he perceives it from outside, as in the case of every other movement, but appraises it as an effort from inside, where the trace also was visible.
The metaphysician obtains this direct perception, which is both internal and certain, only for the movement that he accomplishes for himself. From this alone he can guarantee that they are real acts, constituting absolute movement. Already for the movement accomplished by other living beings, it is not by virtue of a direct perception, but by sympathy; it is for reasons of analogy that he would give them the status of independent realities."
(D & S, pp.38-39)
The passage from physics to metaphysics is here accomplished without violating the requirements of the absolute reality of movement. The position involved is summed up strikingly by Bergson:
"The movement that it (i.e. science) studies is therefore always relative and cannot consist of anything other than what is reciprocity of displacement .... Descartes marked with precision the point of view of science .... He went even beyond the science of his time, beyond Newtonian mechanics, beyond ours, formulating a principle to which Einstein gave a demonstration."
(D & S, pp.39-40)
In this last sentence of Bergson´s he is only reiterating what we have already quoted him as saying before about Einstein being the continuator of Descartes. The relation between space and movement is brought out by Bergson as follows:
"Descartes stated that everything relevant to physics was spread out in space. By this he gave the ideal formula of a universal mechanism."
Thus placing the demi-Relativity of Einstein, Bergson is able to bring us to the point of accepting an idealist and universal mechanics which is basically the same as what modern physics could legitimately accept. Relative motion in the visible world and its inner and outer vibrations and movements when related to discrete bodies can be realistically visualized, irrespective of the requirements of physics or metaphysics. The structure of universal space when viewed as it were from inside can also be reconstructed by us without violating epistemological laws or norms.
Whether we think of a universal observer with measuring instruments seated at the apex of a pyramid-like structure or situated at every point of space, the vision of relativistic space will be on the lines elaborated by Bergson, which we have already quoted on pp.148-153 above. This long quotation deserves examination once again so as to enable us to realize all its real and structural implications. Likewise reciprocity, when fully understood, does not reveal the same picture as unilateral Relativity. The reader could reread with profit here our quotation from Bergson found on pages 148-153 above.
11. BERGSON´S THIRD OBJECTION
Bergson's third objection to Relativity theory is that the physicist does not have "Constantly present before the mind the relation between radical and attenuated Relativity." At the end of the previous section we have seen how Bergson was able to arrive at the notion of absolute movement in space as proper to a universal mechanics in terms of what is compatible with the philosophy of science. The res extensa of Descartes corresponds to the horizontal and is given recognition by Bergson. This correlate is a reference for all physical motion when understood in terms of the pure and universal mechanics implied here.
Having settled the question of space by bringing the discussion to the highest degree of abstraction and generalization, Bergson now proposes to give to time and its nature the same kind of philosophical and scientific treatment. He examines time from the two perspectives of what he calls "Spatialized Time" and "Pure Time". Spatialized Time has a horizontal reference and Pure Time a vertical one. Simultaneous instants of time do not refer to real time at all, but represent conceptualized ideas of time which are metaphysical rather than physical. Simultaneity of two instants when verticalized as two points in two distinct fluxes with a "before" and "after" can be represented as continuous lines. This represents time more in the light of a succession of juxtapositions of instants rather than as simultaneous points in time. Spatialized Time is not the same as Pure Time based on our inner sense of duration. This duration is one that is within the common experience of all human beings and is more directly given to perception than the conceptual points of spatialized time on which the theory of Relativity relies.
The fourth dimension derived from such a time is, according to Bergson, nothing but a spatialized metaphysical and conceptual entity with no perceptual element implied in it. The fourth dimension borrowed from Minkowski by Einstein thus falls outside the scope of physics and the paradox which underlines the acceptance of such a space-time continuum is the result of a confusion between pure and specialized time.
Bergson's third objection is therefore to be understood by us as referring to the confusion between. what he calls radical and attenuated Relativity. Radical Relativity refers to the horizontal aspect and attenuated Relativity to the vertical version of the same. Simultaneous instants are proper to the radical view and succession based on continuity of duration, implying a "before" and "after" in a process of flux and involving memory or future virtual possibles is the verticalized version. Each person can privately feel time as a general murmur of an eternal duration within him in subjective and abstract psychological terms. He can represent it as a measurable positive content in a spatialized and schematic form. Both times can be included under one and the same schematic representation.
Pure Time can be represented as a vertical line in which the past, present and future organically belong together. Subjectivity and objectivity can be cancelled out into a sense of actual duration in which the experienced past and the virtual future have between them a complementarity and reciprocity. The Pure Time of Bergson is an abstraction and generalization of spatialized time with its own horizontal counterpart. It is not necessary for us to bring out the subtleties of this analysis of the nature of pure Time where Bergson tries to abolish the paradox between the radical and attenuated viewpoints of Relativity theory. We cannot do better here than to give a string of striking quotations so as to confirm what we have just said.
Bergson wants to escape the charge of being called a metaphysician. To him reality is as important as it is to the physicist. He does not want to decide whether all reality is perceptible or not. He only wants to maintain that time as a reality is at least on par with what can be perceived. It is the Theory of Relativity that Bergson accuses of being metaphysical by its acceptance of a fourth dimension, which as he points out, has a conceptual rather than a perceptual status.
As for his own position as a philosopher of science, he takes care to remark:
"We have besides to distinguish between the point of view of philosophy and of science: the former considers the concrete as real, as altogether charged with qualities; the latter extracts or abstracts a certain aspect of things and retains only what is size and what is in relation to size. Happily we have not ourselves to be concerned with anything in all that follows, except the one and only reality, namely time. In these conditions it will be easy for us to follow the rule that we had imposed on ourselves in the present study, which is not to accept anything which cannot be accepted by any philosopher or by any scientist, not even anything which is not already implied in all philosophy and in all science." (D & S, p.34)
Bergson takes a stand which is common to both physics and metaphysics. This is unequivocally clear in the above quotation. It is thus that his methodology fulfils the requirements of an integrated Science of the Absolute.
In the next quotation, Bergson seems to imply that the essence of time implies a "before" and "after" and not absolute simultaneity.
"To tell the truth, it is impossible to distinguish between duration, however short it may be, which separates two instants, and a memory that relates one to the other. For duration is essentially a continuation of what is no more into what is. This is the real time which I want to say is perceived and lived. Duration therefore implies consciousness and we place consciousness at the basis of things by the same reason that we attribute to it a time that endures." (D & S, p.62)
Bergson here explains that a schematic representation of duration by a line has not the same reality as pure duration. He clarifies his position in the following way:
"Listening to a melody with the eyes shut, thinking of it only .... one finds it undivided, the melody or the portion of the melody which you would have replaced in pure duration. In other words, our interior duration, envisaged from the first to the last moment of our conscious life, is something similar to this melody. Our attention can turn away from it and as a result from its indivisibility; but as we try to cut it, it is as if we passed a blade across a flame we would be dividing space only." (D & S, p.62)
We cannot examine in detail this minute analysis of Bergson on the question of the two ways of schematizing time as pure duration and as spatialized time. Instead we will give the most important quotations dealing with this subject.
We begin with the following:
"If I should pass my finger on a piece of paper without looking at it, the movement I accomplish, seen from inside, is a continuity in consciousness, and something of my own flux, that is to say, duration." (D & S, pp.63-64)
The flux is of four different grades. This is clearly seen in the example given below where simultaneity in the Einsteinian sense presupposes an absolute time, which is strictly speaking outside the scope of relativity theory. The fourfold structural pattern is reflected here where we read the following:
"When we are seated on the bank of a river the flow of the water, the gliding of a boat or the flight of a bird are three different things to the uninterrupted murmur of our deeper life, or (they can be) one alone according to our wish. We could interiorize everything, thus having to do with a unique perception in its courses which entrains or drags behind it in a confused fashion the three fluxes; or we could leave the first two outside and divide our attention between what is inside and what is outside: or better still, we could do one or the other at a time, our attention relating together or separating the three flowings, by virtue of the singular privilege which it possesses of being one or many. Such is our first idea of simultaneity. We call something simultaneous because the two external fluxes occupying this same duration where they belong, the one as well as the other, to the duration of an identical third one, which is ours: This duration is nothing but our own when our consciousness is directed only to ourselves, but it becomes equally theirs when our attention includes the three fluxes into one individual action."
(D & S, pp.67-68)
Bergson now goes on to define real time and explains that it has no instants.
"The instant is that which terminates a duration if it should stop. But it does not stop. The real time cannot furnish us the instant; the latter results from a mathematical point, that is to say from space. But all the same without real time the point could not be anything but a point and there would not be any instant. Instantaneousness thus implies two things: a continuity of real time, that is to say, of duration, and of time spatialized, which described by a movement becomes a symbol of time: this spatialized time which consists of points rebounds on to real time and makes the instant jump out of it."
(D & S, p.69)
Bergson continues further on:
"Simultaneity in the instant and simultaneity of the flux, are things quite distinct, but they complete themselves reciprocally. Without the simultaneity of the flux, we should not be able to consider the one capable of being substituted for the other of the three terms: continuity of our interior life, continuity of a voluntary movement which our thought prolongs indefinitely, and continuity of any movement whatsoever traversing space. Real duration and time spatialized would not therefore be equivalent.
(D & S, p.79)
All these above quotations refer to the two perspectives. One of them is vertical and the other is horizontal. Time can therefore be viewed either as measurable or as something that is felt within. Bergson now arrives at the notion of time as a fourth dimension. He does this by mathematically schematizing it without a reality of content. The fourth dimension of Einstein comes to have a mathematical rather than a real status. We read the following:
"Immanent to our measure of time there is the tendency of time emptying itself of its contents into a space of four dimensions where past, present and future are juxtaposed or superposed for all eternity." (D & S, p.79)
Bergson is full of hesitation. when it comes to speaking the proper language of an integrated Science of the Absolute. In company with thinkers of his own generation he avoids the a priori method as well as absolutism as starting points in his speculation. Much of the obscurantism that we find in his arguments arises from this desire to keep company with realistic pragmatists and operationalists.
What is valuable to us however is the fully scientific methodology developed stage by stage in the chapters of his book. A vertical axis of reference implying past, present and future, and absorbing within its scope the possible dimensions of physics is what he is able to arrive at by the end of the third chapter. It is at this point that we are concerned with the correct relation between radical and attenuated time. Attenuated time has a vertical reference. The status of future time is a virtual and conceptual one. The world of objects and events implying a future that is still to unravel itself is thought of by Bergson as entering our consciousness backwards rather than forwards. Such delicate distinctions remain to be clarified in the Chapters to follow.
12. BERGSON´S FOURTH OBJECTION
Bergson's fourth objection is that the relativity theory has not "prepared the mind against a confusion between the two" (i.e. between radical and attenuated relativity).
The interaction and interference of the two kinds of Relativity, described by Bergson as the radical and the attenuated, have to rely on the physics and philosophy of Galileo, Kepler and Newton, presupposing a Euclidean space and as well as a Cartesian cosmology and the mathematical space-time correlates. Bergson has to agree and differ alternately with each or both of them. The argument that he adopts becomes delicate and closely knit, replete with personal examples and equations, manipulated with expert ease. He brings in microbial and sub-microbial clocks and beings, and speaks of rival systems belonging to Peter and Paul who are physicists, the latter accepting philosophy only under the very special circumstances of being shot into outer space within a ball. There are also flat, one-dimensional beings who are used as literary devices by Bergson and who are represented as speaking to each other as "blood brothers." Besides Peter and Paul there are also John and Jack who belong to the horizontal structural poles of reciprocity in terms of spatial perspectives, while Peter and Paul belong to the context of expanding, contracting or multiple times acting as simultaneous instants or dislocated into successive continuities in more deeply perceived time.
All these difficulties presented by Bergson arise from the fact that he does not straightaway adopt the metaphysical notion of the Absolute substance as Descartes did. He is also not willing to accept the full implications of the static, formal and general structuralism of post-Hilbertian mathematics. The Bourbakians are still to be accepted in respect of their extreme structurally-minded predilections. It is therefore no wonder that Bergson relies on his own intuitive genius and originality in developing without a conventional a priori method the argument by which he comes to state finally at the end of his book that Einstein is a continuator of Descartes.
His closely knit arguments and equations are essentially inimitable and we cannot do better than attempt to give the gist of what he wishes to say. In doing so we have to rely on a series of quotations following the order of the book. We do this without trying to add more confusion to his delicate thought by rearranging them in any way ourselves. The reader is sure to find such an abridged text very hard going but in order to preserve these methodological and epistemological contributions of Bergson we feel justified in doing this.
The interference of classical physics with modern notions in physics is a question full of many assumptions and presupposition and Bergson's last three chapters are concerned with meeting this question. The reader has the task of seeing Bergson's own standpoint separately from all others that he incidentally discusses. The overall conclusion of an absolute time will then emerge.
With these remarks we shall now examine the contents of the fourth chapter called "The Plurality of Time." The famous episode used by relativity theorists of a man shot into outer space in a ball who on returning finds his counterpart on earth has aged by 200 years while he has aged only two years falls within the scope of this chapter. It is by replacing unilateral Relativity with a bilateral reciprocity that Bergson is able to restate and revise this famous and rather tall claim. He does this in order to abolish the paradox in favour of a fully common sense view acceptable to both philosophy and physics. We now present the important parts of Chapter Four in summary fashion.
13. THE PLURALITY OF TIMES
Bergson opens Chapter IV as follows:
"Let us finally arrive at the Time of Einstein and let us gather together all we have said by supposing in the first place an immobile ether. There is evidently the world moving in its orbit. The instrument of Michelson-Morley is there when one performs the experiment - one repeats it at different periods of the year and as a consequence for the variable speeds of our planet. Always the ray of light behaves as if the earth were immobile. Such is the fact. Where is the explanation?"
(D & S, p.91)
Continuing with this theme we read:
"In the first place what have they to say about the movement of our planet? Would the earth be, in an absolute sense, in movement across space? Evidently not; we are in the hypothesis of Relativity and there is no absolute movement in it. When you speak of the orbit described by the earth, you are placing yourself in a point of view chosen arbitrarily, which is that of the inhabitants of the sun (in a sun which has become inhabited). It is at your pleasure that you adopt this system of reference. But why should a ray of light thrown on the mirrors of the Michelson-Morley apparatus take any notice of your fantasy? If all that is produced in effect is the reciprocal displacement of the earth and the sun, we could take for a system of reference the sun or the earth or any other observatory. Let us take the earth. The problem disappears for it (the earth). There is no occasion to ask while the fringes of interference conserve the same aspect, why the same result is observed at whatever moment of the year. It is just simply because the earth is immobile."
(D & S, p.92)
Bergson explains how between the observer on the sun and one placed on the earth there is a question of having somewhere a reference which is not his own. Each of these physicists would put the question of movement with reference to what he is not (The man on the sun chooses the earth as a reference and the man on the earth chooses the sun). Peter and Paul, when placed in two systems S and S´ as before, Bergson explains, would each have a reciprocal recognition of some system of reference:
"Now there is no more absolute movement, and as a consequence there is no absolute repose of the two systems which are in a state of reciprocal displacement. Each of them would be immobilized in turn by the degree which would raise it to the status of a system of reference." (D & S, p.93)
The two physicists in S and S' conduct the Michelson-Morley experiment and derive from it some information about light and its velocity representing only half its total reality. The paradoxical situation between the two physicists, each of them treating their own system as immobile and real and the other as a mere reference, is brought out by Bergson in the following way:
"But the physicist in the system S´ would proceed in exactly the same way. Declaring himself immobile he would repeat from S all that his fellow physicists placed in S would have said about S'. In the mathematical representation of the universe which he would construct, he would treat exact and definite the measurements he would have taken in the interior of his own system, but he would correct according to the formula of Lorentz all these measurements taken by the physicist attached to system S.
(D & S, p.95)
"Thus two mathematical representations of the universe would be obtained, totally different from each other, if one considered the numbers that figured in each but identical, if one should take account of the relations which are indicated by them as existing between the phenomena, - relations which we call the laws of nature. What is more, this difference is the very condition of their identity. When one takes diverse photographs of an object by turning round the object, the variability of the details does nothing more than translate the invariability of the relations which the details have between them, that is to say, the permanence of the object."
(D & S, p.95)
Bergson now sums up the definite implications of Relativity when reciprocity is fully recognized:
"We are thus brought back to a multiplicity of Times, to simultaneities which will be successions, and successions which will be simultaneities and to lengths that should be considered differently according to their being considered at rest or in movement. We are now facing the definitive form of the theory of Relativity." (D & S, pp.95-96)
Bergson now compares the status of the time taken by systems S and S' as understood by the respective physicists within each system. The reciprocal movement between the two systems can be thought of as taking place horizontally, while the measurement of time can be thought of as taking place vertically.
Bergson refers to this perpendicular reference (the vertical axis) as follows:
"We shall suppose therefore that the physicist is only interested in the line of light ....placed perpendicularly to the reciprocal movement of the two systems." (D & S, p.96)
He then goes on to say that both the physicists concerned belong to system of reference which have between them an interchangeable status:
"But if S' is a double of S, it is evident that the Time lived or acted by the second physicist during his experiment in system S', judged by him as immobile, is identical to the Time lived and acted by the first physicist in system S, equally considered immobile because S and S' once immobilized are interchangeable. Therefore the time lived and counted in the system, the time that is anterior and immanent to the system is the real time and is the same for S and S'." (D & S, pp.96-97)
Bergson further discusses time that is considered paradoxical and mathematical time. He compares and contrasts the times of both the "physicists":
"Thus, in summary, while the time attributed by Peter to his own system is the time lived by him, the time that Peter attributes to the system of Paul is neither the time lived by Peter nor the time lived by Paul, nor a time that Peter conceives as lived or one that could be lived by Paul as a conscious and living being. What would it be other than a simple mathematical expression, destined to mark that it is the system of Peter and not the system of Paul which was treated as a system of reference" (D & S, p.100)
Bergson now resorts to a striking and familiar example of two men painting a picture of two persons placed at a distance. The perspective in the painting corresponds to the distance. The person nearest to the painters appears bigger than the other person. The change of perspective by the painter and the consequent change of size will not really affect the size of the persons concerned. This is also true with the times recorded in their pure mathematical systems. Returning to the two systems, the one mobile and the other immobile, Bergson says:
"But by immobilizing my system I have mobilized the others; I have mobilized them diversely. They have acquired different speeds. The more the speed, the more it is distant from my immobility. It is this greater or lesser distance of their speed to my speed, which is zero, that I express in my mathematical representation of the other systems when I count their times as more or less slow which are always longer than mine, in the same way as it is the greater or lesser distance between Jack (the shorter subject of the painter) and myself which I express by reducing his height.
The multiplicity of times does not exclude the unity of real time; it would rather presuppose it, in the same way as the diminution of height with the distance of a series of canvases where I would represent Jack, more or less distant, would indicate that Jack conserves his own size.
(D & S, pp. 101-102)
Bergson now examines the claim often put forward by followers of Einstein who say that a man shot from a cannon at a very high speed into space, on returning to Earth will find his friend to have aged by 200 years while he aged only two years. When the reciprocity between Peter and Paul is fully accorded, Bergson says such a claim is then untenable.
"The movement being reciprocal, the two personages are interchangeable. (D & S, P.103)
Bergson goes on to explain how physicists and philosophers are naturally obliged to take a differing point of view, even when faced with the same data. A physicist is more interested in the real rather than the theoretical aspect of the situation. He is obliged therefore to treat individually Peter and Paul as real and never theoretically. Bergson, speaking about the physicist says;
"If he is with Paul he will concede to him the time that Paul himself counts. That is to say, the time which Paul effectively lives; and to Peter the time that Paul would attribute to him. But once more he would necessarily choose for Peter or for Paul."
(D & S, p.104)
"In effect both Peter and Paul have to do with the same physics. They observe the same relations between phenomena and in nature they find the same laws. But the system of Peter is immobile while Paul's is mobile. As long as we have to do with phenomena attached in some manner to a system defined by physics in such a way that the system in motion is considered as having them as a consequence, the laws of these phenomena should evidently be the same for both Peter and Paul: the phenomena in motion being perceived by Paul are animated by the same movements as they are immobile to his eyes, and appear to him exactly as they would appear to Peter in the phenomena analogous to his own system. But the electromagnetic phenomena present themselves in such a manner that one can never, when the system where it is produced is considered to be moving, consider them as participating in the movement of the system. However the relations between these phenomena and their relations with the phenomena consequent on the movement of the system are still for Paul what they are for Peter.
If the speed of the ball (the man referred to earlier as being shot into outer space) is really what it is supposed to be, Peter could not express this persistence of relationships except by attributing to Paul a Time a hundred times longer than his own, as one could see according to the equations of Lorentz. If he counted otherwise, would he not be inscribing in his mathematical representations of the world that Paul in movement finds between all phenomena, including electromagnetic phenomena, in the same relations as that of Peter in repose would affirm implicitly that Paul as one referred to could become Paul referring; for why should relations be conserved for Paul, and why should they be marked by Peter or Paul in such a way as they appear to Peter, if it is not because Paul would describe himself as immobile by the same right as Peter? But this is a simple consequence of the reciprocity which he notes, but not reciprocity itself. Once more he makes of himself one who refers, and Paul is nothing but one who is referred to. In these conditions the time of Paul is a hundred times longer than that of Peter. But it is a time that is attributed and not a time that is lived. The time lived by Paul would be his Time as referring and not a time referred to: it would be exactly the time which Peter comes to find." (D & S, pp.105-107)
Bergson now shows how to distinguish real Time from fictitious Time:
"What in effect is a real Time if it is not a Time that is lived or which could be lived? What is an unreal, auxiliary and fictitious Time if it is not that which could not be effectively lived?" (D & S, p.107)
The origin of the confusion between these two Times is now explained by Bergson. Mathematically speaking there is a freedom of choice between two systems of axes by actually choosing one of them in preference to the other. What is chosen becomes a privileged system. Bergson explains:
"In the mathematical usage that one adopts, it is indiscernible in an absolutely immobile system. Thus we see why unilateral relativity and bilateral relativity are mathematically equivalent, at least in the case which concerns us. The difference exists here only for the philosopher, it reveals itself only if one should ask what reality, that is to say, what thing perceived or perceptible is implied in the two hypotheses. The older one is of a privileged system in a state of absolute repose, and will end in posing multiple and real Times.
Peter, who is really immobile, would live through a certain duration; Paul, who is really in movement, would live through a duration which is slower. But the other, which is that of reciprocity, implies that the slower duration should be attributed by Peter to Paul, or by Paul to Peter, according to whether Peter or Paul are referent or reference. Their situations are identical; they live one and the same Time, but they attribute reciprocally to each other a Time that is different to the former and they express in this manner, according to the rules of perspective, that the physics of an imaginary observer in motion should be the same to that of a real observer at rest. Therefore in the hypothesis of reciprocity, one has at least as much justification as commonsense in believing in a unique Time: the paradoxical idea of multiple Times imposes itself only in the hypothesis of a privileged system. But once more, one could not express oneself mathematically except in the hypothesis of a privileged system, even when one has commenced by proving reciprocity."
(D & S, p.107-109)
While the physicist Paul adhered to his own privileged point of view, Bergson remarks:
"Basing his belief on such a physics, Paul will enter into the ball. We will see while en route that philosophy was right. The hypothesis of the traveler enclosed in a ball who lived only two years while 200 years were passed on Earth, was put forward by M. Langevin in a communication to the Congress of Bologna in 1911. This hypothesis which is universally known and quoted everywhere is mentioned in particular in the important work of M. Jean Becquerel on page 52 of "Le Principe de la Relativité et la Théorie de la Gravitation". Even from the point of view of pure physics it is raising certain difficulties, for we are, in reality, no longer confronted with the theory of Restricted Relativity. From the moment that speed changes its direction there is acceleration and we are confronted with a problem of Generalized Relativity.
In any case however, the solution given above removes the paradox and suppresses the problem. We are taking advantage of the opportunity offered here to say that it was the communication of M. Langevin that earlier drew our attention to the ideas of Einstein. It is a known fact how much all those who take an interest in the theory of Relativity owe to Langevin, his works and his teaching."
(D & S, p.109-110)
Bergson explains the theoretical position of the relativist and points out that he has a right not given to earlier physicists which consists of treating his own system of reference as being equivalent to all other possible systems of reference.
He emphasizes this as follows:
"It is exactly because his method of research and his procedure in notation assures him of an equivalence between all the presentations of the universe, taken from all points of view, that the has the absolute right (hardly afforded him in older physics) to hold on to his personal standpoint and to relate everything to his unique system of reference."
(D & S, p.110)
Bergson further explains that in the light of the limited theory of Relativity there is a system of reference treated as independent of the system belonging to observed things. By interaction these two give rise to a confusion which he brings out in the following way:
"What is real is measured by a physicist who is real; what is false is represented in the thought of the real physicist as measured by the false physicist."
(D & S, p.110-111)
Bergson says the physicist has to be a man with a consciousness of his own before being a physicist. Thus Peter might concede to any number of other physicists the right to exist as physicists in relation to their own system of reference at any and all points of the universe. We read the following:
"Inasmuch as he is a physicist he is anterior to the system where he takes his measurements and to which he relates all things. Like himself they are also physicists again and, as a consequence, conscious like himself they would be, strictly speaking, men attached to the system: they construct in effect with the same numbers the same representation of the world taken from the same point of view; they are also referring. But the other one would not be anything but referred to; they could not now be for the physicist anything other than empty puppets. If Peter should concede to them a soul he would lose at once his own; from being referred to they could be referring; they will be physicists and Peter would have to make himself a puppet in his turn."
(D & S, p.111-112)
Bergson points out that the two systems S and S' which he has been considering as duplications, are more compatible with a theory of Relativity rather than with the physics anterior to it.
This he considers paradoxical:
"The two persons in S and S´ could be brought by our thought to coincide together as two figures which one could superpose. They should coincide not only in respect of the diverse modes of 'quality' because their interior lives have become indistinguishable .... Let us simply say that the two observers in S and S´ live exactly the same duration and that the two systems thus have the same real Time."
(D & S, p.114)
Bergson now asks a question:
"Is it the same even in respect of all systems in the universe?"
(D & S, p.114)
If the reciprocity between a series of systems is considered, the principle of immobility implied might have "different intensities of immobilities." But this according to Bergson would not change the overall position. He takes a simpler case:
"Even when one simply accepts the hypothesis that one ordinarily makes when one makes an imaginary observer walk across the world and when one judges oneself the right to attribute to him everywhere the same duration, and understands by this that he sees no reason to believe the contrary .... In other words, the idea of posing a plurality of mathematical Times never came to the mind before the theory of Relativity; it is therefore uniquely to this latter notion that one would refer in order to doubt the unity of Time."
(D & S, p.115)
The equality of status even in this universalized context enhances the value of the theory of Relativity instead of detracting from it; Bergson says:
"Let us conclude when all is said in what concerns the universality of real Time that the theory of Relativity does not shake the admitted idea (of a universal Time), but tends all the more to consolidate it."
(D & S, p.116)
Coming now to the question of succession and simultaneity in time, Bergson points out that when two clocks are adjusted to record the same time it has to refer to an event anterior to it. Intuition comes into play when. tallying an event and a clock, P"
In this connection we read:
"Or, the simultaneity of an event with the indication of a clock which gives the time depends on no adjustments of events on clocks; it is absolute."
(D & S, p.116)
Further implications are now explained:
"If simultaneity were only correspondence between indications of a clock and if it was not also and above all a correspondence between indications of a clock and an event, one would not build clocks and nobody would buy them."
(D & S, p.117)
Bergson now points out that it is possible for a theoretician of Relativity to admit an intuitive simultaneity. In a footnote on page 118 he postulates a microscopic being who constructs his own clocks so as to bring into evidence the fact that even if the distance between two clocks should be small there would be room for error as when they are at a distance. In a previous footnote Bergson meets the objection put forward by a scientist when he says we can think of two clocks and two guided microbes placed together at short distances and even sub-microbes with corresponding clocks. Such arguments Bergson points out are only consistent with pre-relativistic physics such as that of the Greeks, and are not proper to a relativism which insists on accepting nothing if not based on direct statements of fact. Simultaneity can be verified by an observer placed at the centre of a system taken to be immobile, both by intuition as well as by indications of two clocks at equals distances from the observer. Thus two kinds of simultaneity, one called scientific and the other intuitive, can exist without contradiction. Bergson further clarifies the systems S and S´ where clocks verify simultaneity of events or vice-versa. When a system is adopted as a system of reference it is immobilized by the very act. The two simultaneities therefore confirm each other.
Further on we read how succession and simultaneity between two systems S and S´ become interchangeable. One is "conventional" (i.e. conventionally idealistic or metaphysical) and the other is not. By arranging the two clocks perpendicularly in S' instead. of horizontally, conventional simultaneity accords with visual simultaneity as between clocks.
Bergson further establishes a correspondence between four simultaneities of events in the two systems of reference S and S´. He does this by postulating a "supreme conscience capable of sympathizing instantaneously or of communicating telepathically with the two consciousness," (D & S, p.122) and concludes:
"It is evident there is nothing against it .... one can therefore continue to imagine as in the past, instantaneous sections of a unique Time, and of an absolute simultaneity of events."
Bergson takes note of the fact that when physicists give primacy to only one system of reference, the argument about two sets of simultaneities crumble. Although the physicists might be guided by two clocks adjusted to show simultaneity within their own system of reference, Bergson says:
"This does not hinder the two systems S and S' from having simultaneities that are lived, real and which are not regulated by the adjustments of clocks.
We have therefore to distinguish two kinds of simultaneity, two kinds of succession. The first of them is interior to events, it is part of their materiality, it comes from them. The other is just affixed on to them by an observer exterior to the system."
(D & S, p.125)
Further on we read:
"The first expresses something of the system itself; it is absolute The second is changeful, relative, fictitious .... There is an apparent curvature of simultaneity in succession ....This curvature is just what is required so that the physical laws, in particular those of electromagnetism could be the same to an observer inside the system, situated so to say in the absolute, and for an observer outside of whom the relation to the system could vary indefinitely."
(D & S, pp.125-126)
Continuing on the same lines for the next 33 pages, Bergson finally concludes:
"The two systems are in a state of reciprocal displacement, being interchangeable, because S' is a duplicate of S ' the vision an observer in S has of AB is found to be identical by hypothesis to the vision the observer has in S' of A´B´. How to affirm more rigorously and more absolutely the equality of the two lengths of AB and A´B´"? Equality has an absolute sense only, over and above all conventions of measurement, except in the case where the two terms compared are identical; and one declares them identical from the moment one considers them interchangeable. Therefore in agreement of the limited theory of low Relativity extension cannot anymore really contract than Time can slow down, or simultaneity can dislocate itself effectively. But when a system of reference has been adopted, and by that very fact is immobilized, all that passes in the other systems should be expressed perspectively, according to the distance, more or less considerable, which exists in the scale of size between the speed of the system referred to and the speed which is zero by hypothesis of the referring systems. Let us not lose sight of this distinction. If we make John and Jack stand out fully alive in the picture where one occupies the foreground and the other the background, let us take care not to let Jack have the height of a dwarf. Let us give him, as we would also give to John, normal height.
To sum up, we have only to take up again our initial hypothesis of a physicist attached to the Earth, performing and re-performing the Michelson-Morley experiment. But we shall suppose him above all to be preoccupied with what we suppose as real, that is to say, what he perceives or could perceive. He remains a physicist, he does not lose sight of the necessity to obtain a coherent mathematical representation of the togetherness of things. But he wishes to help the philosopher in his task; and never does his interest detach itself from the moving line of demarcation separating the symbolic from the real, and the conceived from the perceived. He would therefore speak of 'reality' and of 'appearance' of 'true measure' and of 'false measures.' In brief, he would not adopt the language of Relativity, But he would accept the theory. The translation which he is going to give us of the new idea in an older language would make us understand better in what measure we could conserve and in what measure we could modify what we have previously admitted. Therefore turning his apparatus at an angle of 90 degrees, at no period of the year does he observe any displacement of the fringes of interference. The velocity of light is thus the same in every direction, and the same for all velocities of the Earth. How to explain this fact?"
(D & S, pp.158-169)
Bergson now makes the physicist answer first from his own standpoint. He says the problem arises only because the earth is in movement. Bergson asks:
"What is this movement related to?" And the answer is given: if any such point exists it could only be arbitrarily chosen. I am free to decide that the Earth shall be this point, and to relate it in some fashion to itself. When it becomes immobile the problem vanishes.
(D & S, pp.159-160)
According to Bergson, the physicist supposes an actual point, say among the stars, which is a system of reference. This means a fresh difficulty arises. By a physicist's notion he has to admit that he has no right to speak of the equal velocity of light in any direction. The physicist would defend himself by saying that although the spectator from the star should judge his premises false there would not be any fundamental difference between the physics revealed to him and the physicist on earth. Units of measurement might be different, the relational laws remaining the same. The theoretician of Relativity, Bergson continues, resembles a person who presses his eyes so as to produce a certain type of double image. By relating everything to his own particular system of reference, and at the same time wanting to create a universally valid physics, the physicist runs the risk of having to face up to this, at least under some circumstances. Although there is a deformation of spatio-temporal relations due to the choice of the system of reference, the relational framework of the laws do not change. There are certain articulations and relations which are intrinsic to the laws of Nature. They can be verified even by wrongly supposed frames of reference.
Bergson further maintains that the physicist should take care to remember that all observers except himself result from fantasy. They can evoke as many phantoms as they wish and there will be as many as there are velocities in other words, an infinite number. The physicist will discover that all the other observers have fundamentally the same relational structure with slight distinctions The physicist would then be satisfied to continue in his own observatory without being troubled by the others. Bergson asks:
"Was it at all necessary for the theory of Relativity to invoke such rival observers". And replies in the affirmative: "It has served a very good purpose in letting scientific thinking take a forward step."
(D & S, p.165)
Bergson concludes this chapter by asserting that the theory of Relativity enables us to think of two independent systems having an interchangeable status between them. This enables us to claim philosophically a finer degree of certitude that no philosophy could have had without the theory of Einstein. He further points out that the very basis of Relativity depends upon abolishing any one privileged system as preferable to another: "Therefore this theory far from excluding the hypothesis of a unique Time depends on it and gives it a superior intelligibility."
(D & S, p.165)
Bergson has now replaced relative Time with a unique and Universal Time having an absolutist status. We now go on to Bergson´s fifth and final objection.
14. BERGSON´S FIFTH OBJECTION
Bergson´s fifth objection is that relativity theory has not "pressed more closely together the passage from physics to mathematics." Mathematics and physics have to be more intimately pressed together into a unified or integrated whole. This is so that the absolute Time principle will have its necessary setting arising even from the theory of Relativity.
In the fifth chapter we find Bergson bringing together a reference to lines and geometrical figures of light, as well as just plain figures consisting of lines belonging more strictly to pure mathematics. The Theory of Relativity is directly concerned with the limiting constant of the velocity of light. It is in a universe filled with light where relativity tacitly assumes the contraction or expansion of time and space. Visible light is given to the senses and belongs to the perceived and perceptible world of physics. When we speak of the contractions or expansions of visible light or their velocity in terms of time we enter into a kind of abstraction and generalization belonging on one side to the laws of nature implied in the equations of Lorentz. On the other side we are visualizing figures of light subjected to disfigurations or distortions due to expansions and contractions of space and time treated together as reciprocal counterparts. There is an implied structural frame of reference to be presupposed before the formal and structural aspects belonging to the equation and the correlates answering to them can be kept in mind together.
Logistics and semantics are in league with formalized mathematics and a structurally understood Cartesianism. We are called upon to think of absolute Time. This is the underlying philosophical reality as presupposed in language, logic and mathematics based on a priori axioms and postulates. Pressing together the visible physical reality in terms of lines of light with its own a priori counterpart conceived in terms of mathematical lines, is a legitimate stage in our enquiry.
When properly understood in this epistemological and methodological light, truth is revealed by the agreement between physics and mathematics. To put it more simply, we have to remember for the purposes of following intelligently the arguments put forward by Bergson that the Lorentz equations answer to certain geometrical lines presupposing a structural correspondence between visual figures and mathematical formulae having a one-to-one correspondence. Hilbert's formalism is anticipated by Bergson as being capable of going hand in hand with a Bourbakian notion of structuralism.
By his desire to press these two aspects together so as to yield one and the same conviction about the absolute status of time, Bergson reveals himself to be an axiomatic or dialectical thinker who relies on the form or structure of thought language or laws of nature reflected in the equations of Lorentz.
The Lorentz equations are meant to explain laws of nature conceptually and perceptually. The same laws of nature are reflected in the structural figures of light. These figures of light can be pressed together or allowed to expand vertically or horizontally. To use Bergson's own terminology they can expand transversally or longitudinally.
Reciprocity exists in both these two senses and the lines of light are to be treated as elastic to the extent and manner that the application of the Lorentz equations belong to worlds having a Newtonian or Einsteinian limit. Physics is right in being more interested in these variable figures of light. Conventional or traditional metaphysics is right when pure mathematics, not necessarily interested in the realities of life, is axiomatic in content. Neither of these gives us the total picture of absolute truth where life and thought meet without contradiction.
The methodology and epistemology proper to an Integrated Science of the Absolute are present in the arguments of Bergson and are found in this chapter. Bergson gives to Absolute Time a central position in the discussion and this does not detract from the validity of the same arguments when extrapolated and applied to the larger context of a fully integrated Science of the Absolute.
We have also to notice in this chapter that Bergson refers to transversal and longitudinal effects having a bearing on the reality of time. He says they are both derived from the same equations of Lorentz and, after treating them separately, Bergson puts their implications together into one and the same formalized and structural whole. In doing so he has performed one of the neatest of intellectual feats that a scientifically minded philosopher could be expected to perform. He has done this without trying to tamper with or distort pure reasoning for fear of adding further confusion.
For our own interests we shall follow as carefully as possible the steps he takes in the fifth chapter which help to lead to his final conclusions. There is already a vertical line of light representing time rather than space partially emerging to view with at least its negative implications. This is fully clarified by the end of this chapter. Further completion and classification of the notion is found in the remainder of the book. The interchangeability of space and time will also become further evident when we take into account the final verdict of Bergson at the end of the book where he gives Einstein the position of being the continuator of Descartes.
15. THE FIGURES OF LIGHT
Bergson opens the chapter as follows:
"This way of envisaging things will permit us to penetrate more into the theory of Relativity. We have just shown how the theoretician of Relativity evokes, from the side of the vision he has from his own system, all the representations that could be attributed to all the physicists who would see the systems in movement with all possible velocities. These representations are different, but the diverse parts of each of them are articulated in such a way so as to ascertain in the interior of these latter the same relations between them, and to manifest in this matter the same laws. Let us now press together more closely these diverse representations. Let us show in a more concrete fashion the growing deformation of the superficial image and the invariable conservation of the internal relations to the content that the velocity is thought of as increasing. In this manner we shall be taking in living terms a view of the genesis of the plurality of Times in the Theory of Relativity. We shall see the signification as designing itself materially before our eyes. At the same time we shall disentangle certain postulates which this theory implies."
(D & S, p.166-167)
Bergson now makes allusion to the Michelson-Morley experiment, bringing in lines of visible light superposed over the mathematically rigid lines which cross over at right angles at a point C to mirrors at A and B, and then come back to point C. When the apparatus is at rest double lines of light coincide with the rigid mathematical lines, as Bergson points out:
"As soon as we suppose them to be in movement the two figures would dissociate."
(D & S, p.168)
Only the figures of light get deformed and not the rigid lines. The lines of light become broken up and that which goes upwards at right angles to B instead of coming straight back forms an angle when returning. The figure of the horizontal line of light remains the same. Bergson now imagines two possible rival positions, both based on the Michelson-Morley experiment. One is pre-Relativist and the other is post-Relativist.
The pre-Relativist admitting the a priori method treats the rigid lines as real and says, as Bergson puts it:
"It is the rigid figure of space which imposes its conditions on the figure consisting of light."
(D & S, p.169)
The post-Relativist reverses the proposition. It is the figure of light which imposes its conditions on the rigid figures. In other words, the rigid figure is not reality; it is only a construction of the mind; and from this construction it is a figure of light, the only one given, which should furnish us the rules."
(D & S, p.169)
Bergson now says that the physicist who is attached to the Michelson-Morley experiment, if he also remains attached to his own system, has no escape from its direct consequences. Only if we allow him to place himself in an imaginary system outside the one where he is actually present can there be any possibility of distortions in figures of light implying contractions or elongations of times or lengths. Three kinds of possibilities of such distortions are shown by Bergson:
"First, in the transversal effect which corresponds as we shall see to what the theory of Relativity would call a prolongation; the second is the longitudinal effect which is for it a dislocation of simultaneity; the third is the double transversal-longitudinal effect which would be 'the contraction of Lorentz.'"
(D & S, pp.170-171)
In a sub-section entitled "Transversal effect or "dilation of Time"", Bergson now asks us to imagine an infinite series of figures of light starting with the original case where the rigid lines coincided with the figures of light. Such an infinite series of figures of light are possible when we suppose that the observers in system S´ who have a fictitious status can be as many as one wants to imagine, depending on the velocity of the movement of S' along a horizontal line. He gives the example of the opening and closing of a telescopic arrangement and refers to a kind of children´s' toy where one may pull out two rods in opposite directions so as to produce a number of soldiers. When pushed inward they fit into a single soldier. The figures revealed when they do not coincide with the rigid lines are many gradations of distorted visions seen in terms of lines of light. It is when these are again referred back and understood as tallying with the rigid lines that they have full reality. Bergson confirms that there is one real time that acts as a standard even when the figures of light and the rigid lines do not coincide, because of the different velocities of one or the other of the systems.
"We see by this how the theory proceeded as if we had taken for a standard scale of time the double course of the going and coming back of a ray of light between two determined points. But if we should then see intuitively at once the relation of multiple Times to the unique and real Time, not only do the multiple Times evoked by the theory of Relativity not break up the unity of real Time, but also imply and maintain it. The real observer placed inside the system in effect is conscious both of the distinction and the identity of these diverse Times. He lives through time that is psychological and with this Time mixes up all the mathematical Times more or less dilated; for, to the extent that he separates the articulated rods of his toy - that is to say, to the extent he accelerates by his thought the movement of his system, - the lines of light lengthen; but everyone fulfills this same duration that is lived. Without such a unique duration that is lived and without such a Time that is real and common to all mathematical Times, what meaning would it have to say that they are contemporaneously taking place at the same interval? What sense could anyone find for such an affirmation?"
(D & S, pp.:172-173)
Bergson explains how psychological time and visible time, in terms of a line of light, remain identical when a system is at rest. When acceleration gives to the system different lengths of visible time, the observer would still be conscious that the lengthening line only represents time in a conventional sense. As soon as he is aware of such a conventional status it becomes abolished for him in favour of real time coinciding with psychological time.
"Therefore in short, the argument of Relativity signifies here that an observer placed anteriorly to system S representing to himself the system in movement, with all the possible velocities, would see the mathematical time of his system lengthen according to the increase of the speed of his system, if the time of this system would have been confused with the line of light OB, 01, BI, 02 B2 .... etc. All these different mathematical Times would be contemporaneous as much as all of them would belong to the same psychological duration, that of the observer in S."
(D & S, p.174)
Such multiple time according to Bergson cannot be lived by anybody. It would have been the same time merely because the first of the series had a real time reference. One has to forget that all these times took place in the same duration if one should give to the multiplicity of times any separate reality at all. On this question Bergson concludes:
"Retaining for them the name of time I do agree: they would be by definition conventional Times because the measure is of no real or possible duration."
(D & S, p.174)
Examining the further implications, we read: "Let us see in the first place - in contriving to make of Time a line of light, the second effect of the deformation of the figure."
(D & S, p.175)
Bergson's next sub-section is titled "Longitudinal effect or 'dislocation of simultaneity'. He says when an observer in system S says that time is dilated he only means that the clocks do not change but time in the abstract changes. This is further explained:
"They (i.e. the clocks) are found to be in the mind of our observer, retarded more and more in relation to one another to the measure that his imagination accelerates the movement of his system."
(D & S, p.176)
It is only by definition that the two clocks showing the same hour are said to be simultaneous, we read:
"What I wish to say is that it was what originally was equal that has become unequal to what has come to glide in between the two clocks, they themselves not having moved at all."
(D & S, p.176)
Bergson further elaborates the distinction between real time and conventional time. The latter can be telescoped backwards so as to coincide with real time. He explains:
"All these dislocations, all these successions, are therefore virtual; simultaneity alone is real. And it is because all these virtualities, and all these varieties of dislocation take place in the interior of this simultaneity really perceived, that they are capable of being mathematically substituted for it. This does not prevent that on one side there is the imagined of what is purely possible, while on the other side it is the perceived and the real." (D & S: p.178)
We read further on:
"But the fact that consciously or not the theory of Relativity substitutes for time the lines of light, puts into evidence one of the principles of the doctrine."
(D & S, p.178)
Bergson now cites Ed. Guillaume who said that the main contribution of Relativity is to substitute the time of the propagation of light for time derived from the earth's rotation. Bergson also cites Edouard le Roy who thinks that when measurement methods are changed in science great steps forward will be taken in the progress of scientific thinking. Bergson. sums up the significance of such a substitution when he says:
"And as it is of the essence of physics to identify the thing with its measurement, the line of light would be at one and the same time the measurement of time and time itself."
(D & S, p.179)
The plurality of Time conditions Relativity because Time is measured by the propagation of light and varies according to the motion of the system. Plurality of time is therefore a condition natural to Relativity. Bergson says Relativity insists on abandoning any kind of time which has only a virtual existence.
It would be more correct to think of such time in terms of differing lengths of light-propagation within differently moving systems.. This choice has a paradoxical element because, as he points out:
"Real duration continues to haunt us. But this is because it is on the contrary very simple and altogether natural, if one should take for a substitute for time an extensible line of light, And if one should name simultaneity and succession the cases of equality and inequality between lines of light of which the relation between them evidently changes according to the state of repose or movement of the system."
(D & S, p.181)
Bergson now comes to the question of putting together transversal and longitudinal aspects of time. Both might lengthen or contract according to the direction of the movement of the system:
"But these considerations on the lines of light would be incomplete if we should limit ourselves to the separate study of the two transversal and longitudinal effects. We have now to be present at their being composed together.
"We are going to see how the relation which should always subsist between the longitudinal and transversal lines of light, whatever be the velocity of the system, brings with it certain consequences in what concerns its rigidity, and as a result also of its extension. We shall be taking a view in living terms of the interlacing of Space and Time in the theory of Relativity. This interlacing does not clearly appear except when one has reduced time to a line of light. With this line of light which is of time but remains stretched out in terms of space and lengthened in accordance with the movement of the system and gathering itself along its course the space with which it makes time, we are going to understand in concrete terms, in the Time and space of everybody, the initial and very simple fact which translates itself by the conception of a Space-Time of four dimensions in the theory of Relativity."
(D & S, pp.181-182)
Bergson's third sub-section is called "The transversal-longitudinal effect or 'the contraction of Lorentz.''' He works out in detail the implications of the Lorentz transformation. Though it is to be understood in terms of lines of light, it also has its distinct longitudinal implications. He brings out these implications with the help of the Lorentz equations. Simultaneity and succession refer to one or the other of the transversal or longitudinal axes. Bergson concludes this chapter as follows:
"We find once again in this manner 'the contraction of Lorentz.' One sees what contraction signifies. The identification of Time with the line of light results in the movement of the system producing a double effect in time: dilation of the second and dislocation of simultaneity .... In one case as in the other one could say that Time alone (the fictitious Time) is what we are dealing with. But the combination of effects of Times gives us what one calls a contraction of length in Space.
One seizes in its very essence the restricted theory of Relativity. In familiar terms it expresses itself as follows: 'given at rest a coincidence of a rigid line in space with a supple line of light, and given, on the other hand an idealist dissociation of these two figures by the effect of a movement which thought could attribute to the system, the successive deformation of the supple figure of light by differing velocities are all that matter; the rigid figure of space would arrange as best it could.'
"By means of facts we see that if the movement of the system, the longitudinal zigzag line of light should conserve the same length as the transversal zigzag line because the equality of these two times is all-important. As in these conditions the two rigid lines of space, the longitudinal and the transversal, could not themselves remain equal, and it is space that should give in. It will give in out of necessity. The rigid trace in the lines of pure space being considered as nothing but the recording of the global effect, produced by the diverse modifications of the supple figure, that is to say, of the lines of light."
(D & S, pp.185-187)
From the italicized lines of the above sentences it is clear that Bergson still adheres, up to this stage of his discussion, to the restricted theory of Relativity, where Space has primacy over Time. The Time coordinate will be fully inserted in the next chapter. The italicized words above are meant to mark the transition from a spatially understood Relativity to one in which Time and Space belong more intimately together as a continuum and not an amalgam. This we shall presently come to see. We now go on to summarize Bergson's sixth chapter.
16. SPACE-TIME OF FOUR DIMENSIONS
Bergson now examines in detail the epistemological homogeneity, methodological correctness and the mathematical validity of the arguments involved in arriving at a pure notion of a Space-Time of four dimensions which is the title of this chapter. He finds it difficult to justify a jump from the Space-dominated status of the restricted theory of Relativity to one where the Time factor as a physical reality is legitimately inserted without ambiguity, paradox or error.
He comes to close grips with the basic paradox between radical and attenuated Relativity and has attempted to dissolve them in favour of a unitive time acceptable to both common sense and Philosophy. The more we approach the paradox the more subtle, vague and generalized are the physical and mathematical factors involved. Einstein himself, as we have seen in speaking of a unified field theory, thought of this task as one belonging to a bold and imaginative scientific speculator.
The transition from the restricted to the general theory of Relativity is open to question on strict grounds of a unified and homogeneous status for the fields involved in each separate theory. The restricted theory respects the contractions and transformations of Lorentz for possible observation. This is made by physicists for whom time is more Space-like than Time-like. In the general theory the Space-like character of Time is not completely abolished, because as Bergson points out, measurement is the very essence of modern physics, and measurement can only be thought of in spatialized terms. To derive the fourth dimension from the three other dimensions requires the intervention of calculus, trigonometry, conics and analytical geometry. They all refer to the same basic laws of nature relationally understood and reflected in the various terms of equations.
We shall spare the reader the difficulty of following all the arguments based on these considerations in detail. Even we are not fully competent to enter into the mathematical argumentation with sufficient certitude. Bergson refers to a Superman's consciousness so as to derive the fourth dimension representing time by interposing such an imaginary one or by the device of two- and three-dimensional animals as carrying on successive dialogues between themselves. He is able to give us a simpler picture of the transition from a two-dimensional to a three- or four- dimensional situation. He does this by simplifying the situation schematically and assuming a paper and pencil world for the purpose of representing successively the additional dimensions through mathematical reasonings. The two schematic images developed by Bergson within the scope of this chapter refer to a helicoidal spiral with a vertical reference and to a more strikingly original one where a vermicular consciousness is represented as being attached to a vertical parameter representing Time. This last schematic image interests us because Bergson holds it in so high a regard that he wants it to be used as an instrument of research.
Bergson also speaks of a tetrahedron with a conscious observer at the summit. It is legitimate for us to suppose that he came very near to visualizing in general the same kind of structuralism that we have ourselves developed in these pages so far. We have referred to this structuralism in the name of linguistic communicability, stressing that it has no reality of its own. A fully formalized semantics, logistics and mathematics will answer to the same structure reflecting laws of thought and nature.
Such is the position we have to presuppose throughout the pages that follow in order to give a methodological and epistemological unity to the present study. Time, causation or any other topic of philosophical import can be given the same treatment as Bergson has done here with the notion of duration.
We can also think of specific or generic times without basic contradiction between them. According to Bergson, as we shall soon see, Time in the most generalized terms as a fourth dimension, requires the consciousness of Superman, who resembles a clever mathematician. Sub-human animals easily appreciate the world of two dimensions and humans the world of three dimensions.
Such are some of the presuppositions in the rest of the work. We shall extract only those points that interest us directly, while avoiding the intricacies natural to the subject.
Bergson opens Chapter Six by leaving aside the figures of light and the distinctions made between the multiplicity of times and psychological time, which opened the door to us for a closer examination of the nature of Space-Time. Let us now take up his considerations in the matter.
Passing on to the notion of Space-Time as understood by Minkowski, and pointing out a subtle distinction concerning the relation of things to their expressions, Bergson explains:
"The thing is what is perceived; the expression is what the mind puts in the place of the thing so as to submit it to calculation. The thing is given in a real vision; the expression corresponds at the most to what we call a fanciful vision."
(D & S, p.189)
Bergson now shows how, when one thinks of a fanciful figure, such an idea is built around something more real at its core, but the way of thinking in Relativity gives to the thing and its expression the same epistemological status. When we are asked to think of the Space-Time continuum of Minkowski is it a metaphysical rather than a physical entity that is implied? Bergson asks how this idea originated.
He next enters into a strenuous and elaborate discussion supported by different equations justified by the Lorentz transformation. He is conscious of the heaviness of the reasoning involved. His main purpose however is simple. He places an observer in system S´ who witnesses two events within the system separated by two points A'B'. In doing this he takes care to respect the mathematics already accepted in respect of Lorentz´s transformations. Bergson is able, when putting the system S´ in relation with the original immobile system S, to arrive at an invariant factor implied between them. Having established such a common factor, Bergson continues somewhat apologetically:
"Our calculation should have appeared somewhat awry. It is really so. Nothing would have been more simple than to have stated straightaway that (x2-x1)2 plus (y2-y1)2 plus (z2-zl)2 – c2 (t2-tl)2 does not change when one submits the transformation of Lorentz to the terms composing it.. It would have amounted to putting on the same rank all the systems where all the measurements are supposed to have been taken. The mathematician and the physicist have to do this because they do not seek to interpret in terms of reality the Space-Time of the theory of Relativity, but merely to utilize it. On the contrary our own subject is this very interpretation." (D & S, p.195)
Bergson next states that whatever is observable to a real physicist in S´ has necessarily to be given a central position in relation to all others which represent an endless variety of distortions or alternations of lines of light. We read: "Alteration and deformations coordinate between themselves in such a manner that certain relations among the measurements remain the same."
(D & S, p.195)
"Now if we fix our attention on this central observer in S´, we have to concede the necessity of establishing, as Bergson says, "a distinction between the case where an observer in S´ would, perceive as simultaneous the events in A' and B', and also the case where he would note them to be successive."
(D & S, pp.195-196)
This double feature is important to recognize because by treating these two cases as mere disjunct particular instances chosen from among possible ones the signification of these two views for purposes of our own desire to clarify the four-fold structure of Time-Space would have been lost.
The pre-relativist three dimensional space relations are now considered. Bergson shows by elaborate calculations how a fourth dimension can be legitimately introduced as required by the theory of Relativity. He relies on the differential calculus and imaginary numbers such as the square root of -1, corresponding to the Time axis. He further justifies a sort of Space-Time amalgam good enough for relativity theory, By further use of the integral, differential and infinitesimal calculi, Bergson is able to permit the notion of Minkowski's Space-Time continuum, treated as an interval of spatialized time moving along an imaginary axis which is timelike, as having the status of what is represented by the square root of -1.
"We have come to see how the notation of a fourth dimension gets introduced, so to say automatically, in the theory of Relativity. From it undoubtedly comes the opinion often expressed that we owe to this theory the first idea of a fourth dimension englobing Space and Time. What we have not yet sufficiently noted is that a fourth dimension of Space is suggested by all spatialization of Time, it has therefore always been implied by our science and by our language. One can even extract it out in a more precise form, at least in a more figured way from the current conception of Time, than from the theory of Relativity. Only in the current theory the assimilation of Time into a fourth dimension is understood, while the physics of Relativity is obliged to introduce it into its calculations. This comes about from the double effect of endosmosis and exomosis between time and space, resulting in the reciprocal stepping over of one into the other, which seems to translate the equations of Lorentz. It becomes necessary here to situate and to implicitly indicate its position in time as well as in space. It remains no less true that the Space-Time of Minkowski and Einstein is a species of which the common spatialization of Time in a space of four dimensions is the genus.
The course that we have to take is therefore completely traced. We should commence by asking what it is that signifies in a general manner the introduction of a context of the four dimensions which would reunite Time and Space. Then we would ask what we add to it or what we take away from it when we conceive of the relation between spatial and temporal dimensions after the manner of Minkowski and Einstein. Even now we get a glimpse of the question of whether the current conception of a Space accompanied by a Time spatialized naturally takes in the mind the form of a context with four dimensions. If this context is fictitious in that it simply symbolizes the convention of spatializing time, it would even be so for the species, for which the context with four dimensions would be the genus.
In all cases species and genus would have without doubt the same degree of reality and the Space-Time of the theory of Relativity would probably not be more incompatible with our older conception of duration which is not anything more than a Space-and-Time of four dimensions, symbolizing at once the usual Space and Time spatialized. Nevertheless we cannot dispense with considering more specially the Space-Time of Minkowski and Einstein when once we would have occupied ourselves with a general Space and Time of four dimensions. Let us attach ourselves to this first of all."
(D & S, pp.199-200)
In examining the merits of the fourth dimension introduced by Relativity as an artifice adopted for purposes of calculation, Bergson now proposes a simpler way of introducing Time as a dimension into Space. He wants to simplify the side of Space, by treating it as two-dimensional as on a piece of paper with two lines crossing at right angles. Bergson explains as follows:
"We have much trouble imagining a new dimension if we take our start from a Space with three dimensions, because experience does not show us a fourth one. But nothing is more simple if it is a Space of two dimensions to which we endow from our side this supplementary dimension. We could bring to mind plain living beings living on one surface and conferring themselves in it, knowing nothing other than two dimensions of space, one of them could have been conducted by his calculations to postulate the existence of the third dimension. Superficially in a double sense of the word, his congenital brother would refuse to follow him; he would not succeed in imagining what his understanding could have conceived. But we, who live in a Space of three dimensions would have the real perception of the fact that it would be simply represented as possible; we would take account exactly of what should have been added in introducing a new dimension. And as it would be something of the same kind that we would be doing ourselves, if we supposed, reduced into three dimensions as we already are, that we are immersed in a context of four dimensions we would be nearly imagining in this manner the fourth dimension which appeared to us in the beginning as unimaginable. It is true it would not be altogether the same thing, because the space of more than. three dimensions is a pure conception of the mind and could not correspond to any reality, while the space of three dimensions is that of our experience.
When therefore in what follows we make use of our Space of three dimensions really perceived, to give a body to representations of a mathematician subjected to a flat universe - representations conceivable to him but not what could be imagined - that would not amount to saying that there exists or could exist a Space of four dimensions capable in its turn of being realized in a concrete form from our own mathematical conceptions when they transcend our world of three dimensions. That would be to play too well on the side of those who would interpret at once metaphysically the theory of Relativity. The device that we are going to use has for its unique object that of furnishing our imaginary support of the theory, so as to render it more clear, and by that to enable us to see better the errors into which our hasty conclusions would make us fall."
(D & S, pp.200-201)
Bergson comes back to his starting point by saying that to the two lines at right angles Relativity adds a third perpendicular line:
"To this world of two dimensions the theory of Relativity endows an additional dimension which is meant to be Time .... Surely this additional dimension is altogether of a special nature."
(D & S, p.202)
After positing the special nature of the fourth dimension Bergson once again explains that the theory of Relativity does not give importance to it. We read:
"If it (Relativity) had recourse here to a device, and if it had assumed an imaginary time, it was precisely so that its invariant could conserve the form of four squares, each having the coefficient of unity, so that the new dimension could be provisionally assimilated to the others."
(D & S, p.21)
Bergson goes on to examine what this additional dimension adds and takes away from the original two dimensions. Distinguishing two kinds of Space related to Time, he says:
"The mathematical Time could be treated as an additional dimension of Space."
(D & S, p.203)
Bergson then goes on to develop a complete schematic representation of time understood actually as well as imaginatively:
"Let us suppose a superficial universe reduced to a plane P, and let us consider on it a mobile plane N which describes any kind of line, for example a circumference starting from a certain point which we shall treat as the origin. We who live in a world of three dimensions could represent to ourselves mobile M and drawing with it a line MN perpendicular to the plane and of such the variable length would measure at each instant the time that has passed since the origin.
The extremity N of this line will describe in the Space with three dimensions a curve which would be, in this present case, of a helicoidal form. It is easy to see that this curve traveled in Space of three dimensions would reveal to us all the peculiarities of a temporal nature of the changes that have taken place in the space of two dimensions. The distance of any point from the coil to the plane P would indicate in effect the movement of Time with which we are concerned, and the tangent to the curve at this point would give us by its inclination to the plane P, the velocity of this mobile at that moment. In this way one would say 'the curve of two dimensions' does not sketch more than a part of reality stated to be on the plane P, because it is nothing but space in the sense that the inhabitants of P give to the word. On the contrary the curve of three dimensions contains this reality entirely: it has three dimensions of Space; it would be of a Space-and-Time of three dimensions for a mathematician of two dimensions, who would inhabit the plane P, and who, because he was incapable of imagining the third dimension, would be led by the experience of the movement to conceive it and express it analytically. He could afterwards learn from us that a curved dimension exists effectively as an image.
Once we have posited a curve of three dimensions, which would be Space and Time at once, the curve of two dimensions would appear to the mathematician of the ordinary universe as a simple projection of the latter on the plane which he inhabits. It would be nothing more than the superficial and spatial aspect of a solid reality which should be called Time and Space at once.
In short, the form of a curve of three dimensions informs us here both about the plane trajectory and the temporal peculiarities of a movement taking place in a Space of two dimensions. More generally that which is given as movement in a Space of a certain number of dimensions could be represented as a form in a Space having one more dimension.
But is this representation really adequate to what is represented? Does it correctly contain what the latter contains? We would believe it in the first instance as we have just explained. But the truth is that it includes more by one side and less by the other, and if two things look as if they could be interchanged it is because our mind cuts out surreptitiously from the representation what there is in excess, introducing no less surreptitiously that which is lacking.
Let us commence by the second point. It is evident that the so-called future has been eliminated. That is to say, science has no use for it in the present case. What is its object? Simply to know where the mobile would be at any given moment in its course. It transports itself invariably at the extremity of an interval already severed; it occupies itself only with the result that has been once arrived at: if it could represent at one stroke all the results acquired at all moments in a manner whose result corresponds to such and such a moment, it would have gained the same success as a child who has become capable of reading instantaneously a word instead of spelling it out letter by letter. This is what happens in the case of our circle and our coil which correspond point to point. But this correspondence has no signification except when our mind follows up the curve and occupies its successive points. If we can replace the succession by a juxtaposition, the real Time by a Time spatialized, that which is becoming with what has become, it is because we conserve in ourselves the becoming which is the real duration. When the child actually reads the words at one stroke it spells it out virtually letter by letter. Let us not therefore imagine that our curve of three dimensions reveals to us, so to say crystallized together, the movement by which is traced the plane curve and the plane curve itself. It has simply extracted from the becoming that which interests science, and what is more, science cannot utilize this because our mind will re-establish the future which was eliminated, or it will feel capable of doing so. In this case the curve with N plus I dimension all traced out which would be equivalent to the curve of N dimension in the process of being traced would represent really less than what it claims.
But in another sense it represents more. Cutting out from here and adding on to there it is doubly inadequate.
We have obtained it (i.e. the curve) in effect by a well-defined procedure by the circular movement in the plane P of a point N, which drew with it the line of a variable length MN, proportional to the time that has elapsed. Thus plane, circle, line and movement are the perfectly determined elements of the operation by which this figure was traced. But this figure when completely traced does not necessarily imply this mode of generating. Even if it still implies it, it could be the effect of the movement of another line, perpendicular to another plane of which the extremity M would have described on this plane with quite a different velocity, a curve which was not a circumference."
(D & S, pp.203-207)
Bergson further elaborates in a few paragraphs the implication of the coil in relation to the two-dimensional surface. He shows how there is a plus and minus compensation of perceptual and conceptual factors between them, offering infinite possibilities within its total scope. The child who spells letter by letter and the one who is able to read the word at one stroke belong to complementary or reciprocal aspects of this helicoidal projection which is an amalgam of Time and Space. In this connection we read:
"In adding a dimension to the Space where we find ourselves we could without doubt figure to ourselves by a thing in this new Space a process or a becoming as being present in the old. But as we have substituted something ready-made for what we perceive as being made, we have on the one hand eliminated the future inherent in Time, and on the other hand introduced the possibility of an infinity of other processes by which the thing could have been equally well constructed."
(D & S,p.208)
After discussing what is the more real of the alternative times, Bergson sums up:
"In brief, we forget that, in Time that is measurable, being necessarily symbolized by Space, there is at one and the same time a plus and minus in the dimension of Space taken to be a symbol rather than in Time itself."
(D & S, p.209)
Bergson now brings in the analogy of the cinema (see also Creative Evolution, Ch. 4) by way of referring to two aspects of presented Time. One belongs to the symbolism of science and the other is given to experience. He sums up:
"Certainly the role of absolute determinism in this universe is great; it is precisely because of this that a mathematical physics is possible. But what is predetermined is virtually what has already been ready-made and it does not endure except by its solidarity with what is being made, with what is real duration and what is succession: we have to take account of this interlacing and one would then see that the past, present and future history of the universe could not be considered capable of being globally given along the length of a film."
(D & S, p.211)
Bergson sums up the point of view of two inhabitants of a world of two dimensions extending infinitely. The first is scientifically minded, but the second, having some creative imagination, is able to predict the future. His own standpoint we notice tallies with the latter.
The following extract sufficiently reflects his position:
"We could suppose that it has a third dimension which our senses do not reach and across which our consciousness could travel precisely when it unravels itself in 'Time'. By virtue of this third dimension of Space, all the images constituting all the past or future moments of the universe are given at one stroke with the present image, not disposed as one in relation to the another as in. a photograph along the length of a film (for this in effect would then not be any place), but arranged in a different order, which we would not be able to imagine but which we could however conceive. Living in Time consists in traversing this third dimension, that is to say, to detail it, and to perceive the images one after another which permit themselves to be juxtaposed .... We believe that the images are created to the extent that they appear, just because they seem to appear to us, that is to say, to be produced before us and for us, and come to us. But let us not forget that all movement is reciprocal or relative: if you should see them coming to us, it is also true to say that we are going towards them. They are in reality there; they wait for us in a line: we pass along the front. Let us not say therefore that either events or accidents happen to us - it is we who arrive at them. And we could experience this immediately if we knew the third dimension as we know the others.
Now let us suppose that I am taken as an arbiter between the two camps. I will turn towards those who have just spoken and would tell them: 'let me first congratulate you for having no more than two dimensions. For by this you are going to get for your argument a verification which I would vainly search for myself, if I make a reasoning analogous to yours in the Space that fate has thrown me into. I find in effect, that I inhabit a Space of three dimensions; and when I agree with such and such a philosopher in the matter of there being a fourth dimension, I say something which is perhaps absurd in itself, although mathematically conceivable. A Superman who in my turn I would treat as an arbiter between them and myself would perhaps explain that the idea of the fourth dimension is obtained by the prolongation of certain mathematical habits contracted in our Space (absolutely as you have obtained the idea of a third dimension), but the idea this time does not correspond and could not correspond to any reality. There is nevertheless a Space of three dimensions, where precisely I find myself: it is a good fortune for you, and I am going to be able to give you more information.
Yes, you have justly guessed in believing it possible that the co-existence of images like yours, each one extending on as infinite 'surface,' while it is impossible in the Space cut off where the totality of your universe seems to you to take place and to be contained in each instant. It is sufficient that these images - named by you 'planes' - are piled up as we say one over the other. There they are piled up. I see your universe 'solid', according to our manner of speaking; it is made up of piling together all your plane images, past, present and future. I also see your consciousness traveling perpendicularly to these superposed 'planes,' never taking notice of anything but what it traverses, perceiving as the present, and afterwards remembering the one that is left behind, but ignoring those in front which enter turn by turn into their present to come quickly to enrich their past.
Only this is what still strikes me:
I take any image whatever, or better the films without images in order to figure out your future which I do not know. I have in this manner piled up on the present state of your universe the future states which remain for me blank: they make a counterbalancing weight to the past states which are on the other side of this present state, and which I see as determined images. But I am not at all sure that your future coexists in this manner with your present. It is you who say so, I construct my figure based on your indications, but your hypothesis remains a hypothesis. Do not forget that it is a hypothesis and that it simply translates certain properties of altogether particular facts, cut out of the immensity of the real, in which the science of physics is interested. Now I could tell you by making you the beneficiary of my experience of the third dimension, that your representation of time by means of space would give you at once more or less than what you intended to represented."
(D & S, pp.212-215)
Bergson now pleads for a double-sided correction to be applied to the fourth dimension of Time before it could escape the charge of being merely metaphysical or mathematical on the one hand, and on the other hand, one that is given to the intuitive experience of a superhuman observer. His imaginary superman now speaks:
"I, who am inserted in the world organized by my body, by the world made conscious by my mind, I perceive the onward march as a gradual enrichment, as a continuity of invention and creation. Time is for me what is most real and what is most necessary; that is the fundamental condition of action - I say it is action…."
(D & S, p.216-217)
Further on, Bergson says:
"Do not take me for a metaphysician, if you would call the man of dialectical constructions by that name. I have constructed nothing, I have only stated facts .... what is immediately given should be taken for real as long as one is not convinced that it is a simple appearance; it is up to you therefore if you see an illusion to bring a proof to bear on it."
(D & S, p.217)
Continuing in the same vein, he says:
"The metaphysics of the greater part of the metaphysicians is nothing but the law of the functioning of human understanding, which is one of the faculties of thought, but it is not thought itself."
(D & S, p.218)
In very clear terms Bergson now sums up the nature of Time, as follows:
"It matters little, however, whether you express yourself in one of these ways or in another: in either case there is a plane P - that is Space. -- and a displacement of this plane parallel to itself - that is Time - which makes out that the plane traverses the totality of the block, posited once and for all."
(D & S, p.219)
He finally sums up:
"Such are the two points (viz. of construction or destruction by an architect who is supposed to begin from the top or the base the latter being positive and the former negative) which one should never lose sight of when one joins time to space, in endowing the latter with an additional dimension." (D & S, p.221)
He further underlines this in the following way:
"Whoever does not bring to bear here a double corrective would risk being led to error on the philosophical significance of the theory of Relativity and of erecting a mathematical representation as a transcendent reality."
(D & S, p.222)
Bergson leaves behind the considerations connected with Time joined with Space and treats there both as an amalgam. We read:
"But now we should occupy ourselves with the special aspect which the fourth dimension takes in the Space-Time of Minkowski and Einstein."
(D & S, p.223)
The fourth dimension cannot anymore be considered on a par with the three others. The fourth dimension would be affected by the velocity of light having a different status. Mathematics recognizes the imaginary nature of the fourth dimension. If we finally put them together giving a particular form of Space and Time we get to know this as an amalgam. In the beginning, the theory of Relativity seemed to accept a plurality of Times, but when we look at its implications we find Bergson telling us otherwise:
"On looking at it at closer quarters we have never found anything but one real Time, that of the physicist who constructs science - the others are virtual Times, that is to say, fictitious, attributed by him to virtual observers, that is to say, fanciful. Each of these fanciful observers becoming animated all of a sudden, would place himself in the real duration of the older real observer, who has become fanciful in his turn."
(D & S, p.224)
Thus both the mobile and the immobile observers have a virtual status proper to, and most suited for, explaining electromagnetic phenomena through the equations of Lorentz. The physicist who is actually experimenting has to abandon his place in favour of a physicist imagined to be experimenting before a proper mixing of Time and Space can take place even for the purposes of Einstein´s relativity. Bergson says:
"That is to say, he would not know how to abandon it without installing himself in another system: the latter which is thus at rest will have a Space and a Time clearly distinct from ours. In the same way Space could swallow up Time, and Time which in its turn could absorb Space, are Time and Space always virtually and merely thought of, and never actual and realized. It is true that the conception of such a Space-Time will act on the perception of actual Space and Time. Traversing Time and Space which we have always known to be distinct and by that very reason amorphous, we shall be able to see as if by transparency an organism of Space-Time articulated. The mathematical notation of these articulations effected on a basis that is virtual and carried to its most high degree of generalization will give us an unexpected hold on reality. We shall then have in our hands a powerful means of investigation, a principle of research which we can predict even from the present as one that the human spirit will not renounce, even when experience should impose a new form to the theory of Relativity.
To show how Time and Space do not begin to interlace at the moment when either one or the other becomes fictitious, let us return to our system S´ and our observer, who placing himself effectively in S´ transports himself in thought into another system of S.
Now immobilize it and suppose S' to be animated by all possible speeds. We wish to know in the theory of Relativity what signifies the interlacing of Space and Time considered as an additional dimension.. We shall be changing nothing in what results and we shall be simplifying our exposition in supposing the space in our systems S and S' to be one unique dimension which is a straight line, and that the observer at S´ having a vermicular form occupies a portion of this line."
(D & S, pp.225-227)
The relation between pure Space which is real with an amalgam of Space-Time which is bound to be virtual is also explained:
"But this reality could be virtually reconstituted by an amalgam of virtual Space and Time. This Space and Time as imprinted on the system by the observer who idealistically detaches himself from it, lengthens to the extent that the virtual velocity increases. In this manner we obtain an infinity of amalgams of Space and Time, as merely thought of, all equal to pure and simple Space, perceived and real.
But the essence of the theory of Relativity is to place on the same rank the real and the virtual visions. The real world would not be other than a particular case of the virtual." (D & S, p.229)
Further clarifying the relation between real Space and Space-Time we read:
"We are thus brought back to our earlier conclusions. We have been shown that to the person who observes them in the interior of his system two simultaneous events would become successive for the one who would represent them from outside the system in movement. We have agreed but we took note of the fact that the interval between the two events which have become successive, could well be called time, and could contain no event.
This we have said was 'nothingness dilated.'"
(D & S,p.230)
In concluding this chapter Bergson finally explains the nature of Time and Space interpenetrating each other:
"For this Space and Time which interpenetrate are not the Space and Time of any real physicist or even conceived as such. The real physicist takes his measurements in the system where he finds himself, which he mobilizes in adopting it as a system of reference. Time and Space rest distinct therein, impenetrable to each other.
Space and Time interpenetrate only in a system that is in movement where the real physicist is not present, and where only the physicist imagined by him lives - imagined for the greatest benefit of science. But these physicists are not imagined as real or as capable of being so: to suppose them to be real and to attribute to them a consciousness would be to erect this system as a system of reference, to transport oneself there and to confound oneself with them; in any case to declare that their Time and Space have ceased to co-penetrate.
We come back in this manner by a long detour to our starting point of Space convertible into Time, and of Time reconvertible into Space, and we simply repeat what we already have said about the plurality of Times, succession and simultaneity, taken to be the same thing in the two Cases. The invariance of the expression dx2 plus dy2 plus dz2 minus c2dt2 immediately results from the equation of Lorentz. And the Space-Time of Minkowski and Einstein does nothing other than symbolize this invariance, just as the hypothesis of multiple Times and simultaneities which are convertible into successions do not do anything more than translate these equations."
(D & S, pp.234-235)
The application of the Lorentz equations to the varying mathematical and physical reciprocal velocities of the systems do not affect and change the two-sided structural status. Bergson's epistemology and methodology agree with our own. If Einstein's position is enlarged upon and extrapolated into more generalized philosophical terms by Bergson, we on our part can extrapolate by the same token the revised double status of time into the general context of an Integrated Science of the Absolute. There is no violation of principle in doing this.
In Bergson's "Final Remarks," we find an attempt is made to put together the restricted and general theories of Relativity. This is done so that they can belong consistently together correctly, for a more complete and absolute thinking substance referable to the two structural Cartesian correlates. All the other arguments justifying the pressing together of physics and mathematics recommended by Bergson need not be gone into here. The loose ends of his developing arguments are ultimately gathered together by Bergson himself in his "Final Remarks," which we now quote in full.
17. THE TIME OF THE RESTRICTED THEORY OF RELATIVITY AND THE SPACE OF THE GENERAL THEORY OF RELATIVITY
"Here we are at the end of our study. It had to refer to the Time or the paradoxes concerning Time which one ordinarily associates with the theory of Relativity. It will be limited to restricted Relativity. Do we remain for this reason in the abstract? Certainly not. And we would have nothing essential to add on to Time if we introduce into simplified reality, with which we were occupied till now, a gravitational field. According to the theory of general Relativity, we cannot in a gravitational field define the synchronization of clocks nor affirm that the velocity of light was constant. As a consequence, strictly speaking, the optical definition of time disappears. As soon as we wish to give a sense for a time coordinate we would necessarily be placed in the conditions of a restricted Relativity in going according to need to see for it in infinity.
At each instant a Universe of restricted Relativity is tangential to a Universe of general Relativity. On the other hand we have never to consider the velocities comparable to that of light nor the field of gravitation which would be intense in proportion. Therefore in general terms we could, with a sufficient approximation, borrow the notion of Time from restricted relativity and conserve it as it is. In this sense Time pertains to the Restricted Theory of Relativity as Space does to the General Theory of Relativity.
Much is needed to bridge the Time of restricted Relativity and the Space of general Relativity for each to have the same degree of reality. A profound study of this point would be singularly instructive to the philosopher. It would confirm the radical distinction of nature which we established once before between real Time and pure Space, unduly considered as analogous by traditional philosophy. And perhaps it would not be without interest for the physicist. It would reveal that the restricted and the General Theories of Relativity are not animated by exactly the same spirit, and have not altogether the same significance. The first has besides come out of a collective effort, while the second reflects the proper genius of Einstein. The former brings us above all to a new formula for results already acquired; it is truly in the proper sense of the word a theory and a mode of representation. The latter is essentially a method of investigation and an instrument of discovery. But we have not here to institute a comparison between them. Let us say only a couple of words on the difference between the Time of one and the Space of the other. This would be returning to an idea many times expressed in the course of the present study.
When the physicist of General Relativity determines the structure of Space, he speaks of a Space where he is effectively placed. All that he advances, he would verify with appropriate instruments of measurement. The parts of Space of which he defines the curvature can be as distant as one could wish: theoretically he would transport himself there, and theoretically too he would make us witness the verification of his formula. In brief, the Space of General Relativity presents some peculiarities which are not merely conceived and which could be as well perceived. They concern the system where the physicist lives.
But the peculiarities of time and notably the plurality of Time in the restricted theory of Relativity, escapes not only in fact the observation of the physicist who posits them: they are unverifiable in principle. While the Space of General Relativity is a Space where one is oneself, all except one of the Times of Restricted Relativity are defined in the manner of being Times where one is not present. One could not be present there, because one carries with oneself wherever one goes, a Time that chases the other, like the torch attached to a man who walks, making the mist recoil at every step. One does not even conceive oneself as being there, for to transport oneself by thought which, in one of the dilated Times, would be to adopt the system to which it belongs, to make it one's system of reference; at once this Time would contract and would become again the Time that one lives in the interior of a system, the Time which we have no reason at all not to believe to be the same in all systems.
The dilated and dislocated Times are therefore auxiliary Times, interlaced by the thought of the physicist between the point of departure from calculation which is real Time and the point of arrival which is the same Time again real. In this latter Time one has taken measurements in which one operates; to this would apply the results of the operation. The others are intermediaries between the enunciation and the solution of the problem.
The physicist puts all these on the same plane and calls them by the same name. He also treats them in the same manner. And he is right. All are in effect measurements of Time; and as the measurement of a thing is in the eyes of physics that thing itself, all should be Time for the physicist. But in one case alone among them - we think we have shown this - there is succession. One alone among them endures as a consequence, the others do not endure. While the former is without doubt a time placed back-to-back to the length which measures it, but is distinct from it; the others are nothing but lengths.
More precisely, the former is at one and the same time a Time and a 'line of light'; the others are nothing but lines of light. But as these last lines are born from a lengthening of the first and as the first was stuck on to Time, one could say of them that they were Times lengthened. From this arise all the Times in an indefinite number of restricted Relativity. Their plurality, for from excluding the unity of real Time, presupposes it.
The paradox commences when one affirms that all these Times are realities, this is to say, things that we perceive or could perceive, as one that is lived or could be lived. They have implicitly admitted the contrary for everything except for one only: when one has identified Time with the line of light. Such is the contradiction which our mind can guess, when the mind does not see it clearly. It is not attributable either to the physicist as such: it will only come into view in a physics that would erect itself as a metaphysics. To this contradiction our mind is not equal. We were mistaken to have attributed its resistance to a prejudice coming from common sense. Prejudices disappear or at least become weakened on reflection. But in the present case reflection reaffirms our conviction and even ends up rendering it unshakable, because it reveals to us, in the Times of restricted Relativity - one alone among them excepted - Times which are without duration, where the events would not be able to succeed nor things subsist, nor beings grow old.
Aging and duration belong to the order of quality. No effort of analysis would resolve them into pure quantity. The thing remains here distinct from its measurement, which applies however to a Space representative of Time, more than to Time itself. But it is quite different with Space. Its measurement exhausts its essence. This time the peculiarities discovered and defined by physics belong to the thing and not any more to the view of it taken by the mind. Let us rather say; they are reality itself, the thing is now relation. Descartes brought matter back considered within the instant - to extension; physics in his view attained the real to the extent it was geometric. A study of General Relativity parallel to that which we have already undertaken of Restricted Relativity, would show us that the reduction of gravitation in terms of inertia has just been an elimination of readymade concepts, interposed between the physicist and his object, and between the mind and the constitutive relations of things, obstructed physics from being geometry. Viewed thus, Einstein is the continuator of Descartes."
(D & S, pp 236- 241)
18. AXIOMATIC PHYSICS
Recently, I was presented with a typescript containing a course of lectures entitled: "Rigour, Adequacy and Vigour in Axiomatic Physics". This course has just been instituted at the University of Lyons by Prof. Janin. There was a sentence in the typescript which I found intriguing "To find Bourbaki as being irreplaceable does not rule out the possibility of finding him irritating on first contact."
The attitude contained in this sentence reflects the general state of mind in France when confronted with a certain new and heterodox way in scientific thought. Irritation and interest seem to be the rival reactions most men feel about Bourbaki at present in Europe. Hilbert had formalized mathematics so as to justify the notion of a chose mathématique (a mathematical thing). Side by side with the progress of such formalization there was taking place from the side of the geometry of algebra a process of schematization which presupposed the visible rather than the logical and the perceptible rather than the conceptual aspect of thought.
These two legitimate ways of mathematical abstraction and generalization refer to one and the same central Reality whose scientific certitude is in question. The Pythagoras Theorem represents such a central certitude obtained from visible geometrical construction as well as from algebraic formulation. Formalism and schematism have a rigour, adequacy, and vigour, as referring to axiomatic certitude. This way of thinking is beginning to find its place in a revised scientific epistemology and methodology. One also hears of such expressions as the 'beauty' and 'power' of the new structural notions such as the Gaussian curve of statistical probability.
A one-to-one correspondence between ensembles belonging to a quaternian structure of complex numbers belongs to the same context of axiomatization. A close scrutiny of the passages cited above from Bergson reveals that he was a forerunner who happened to anticipate somewhat prematurely this new way of structural axiomatization.
This new vogue is finally being ushered in by some of the most modern of scientific thinkers, of whom Prof. Janin, whom I met, is an example. The fourfold or fourth dimension comprising them, the double correction, and the endosmosis and exosmosis are meant to take place between physics and mathematics when closely pressed together and more fully integrated as recommended by Bergson. We know that mathematics implies logic and axioms. Mathematical definitions also have a semantic link between them. Laws of nature have an internal structure stated in the form of the logistical language of the propositional calculus. Thus sometimes, mathematics, logic and structuralism can all be considered to belong to the context of this new way of axiomatization in scientific thought.
The Bourbakians are suspect at present and the term has the effect of a nickname rather than that of a respectable school of modern thought. Hence the irritation and hesitancy evidenced by modern nuclear physicists like de Broglie when they had to speak of the epistemological status of the particle or the wave belonging together to a common structural context. The direct disciples of de Broglie, M.A. Tonnelat, and T. Destouches-Fevrier have written about the structural and axiomatic implications of the laws of physics.
Heisenberg and Niels Bohr have their own way of referring axiomatically and structurally to the relation between the a priori and a posteriori aspects of reality. Once the mutual absorption of physics and metaphysics is shown to be possible and legitimate, axiomatization can be considered a natural consequence of the unhindered trend of modern thought. We have already had occasion in our preliminaries to refer to these features initially.
When structuralism is admitted in an integrated manner into a limited laboratory context, it can. be extrapolated and applied to larger and larger fields of thought as the extrapolation passes from the species to the genus of any system of thought.
Time, space and causality can be subjected to such an axiomatized way of thinking whether one is interested in. the unified field of physics or the universally valid field of philosophy. Both can refer only to the same absolute truth.
Dialectics, known to the world from ancient times, is a form of axiomatic thinking where the vertical counterparts absorb or cancel each other without contradiction. When the perspective is turned at right angles some kind of orthogonality and exclusion is implied. This seems to be an inevitable concomitant of structurally based axiomatization. When as Bergson recommends, mathematics and physics are pressed together, a totality results in a kind of homomorphism referring to a common structural pattern wherein conceptual and perceptual aspects of schematized truth coexist without contradiction. In the context of cybernetics, homomorphism is to be replaced with homeostasis which is a kind of equilibrium belonging to a normalized and re-normalized state. We also have thermodynamic equilibrium where entropy and negentropy balance each other. These are some of the idioms referring to aspects of modern scientific thinking which we have to keep in mind throughout this work.
We cannot do better here than to cite at random some extracts from modern axiomatic thinkers. We wish thus to show that the methodological approach of Narayana Guru is the same as that of these thinkers, and above all banish any lingering prejudice about his being some strange oriental mystic quite different from modern thinkers. When Narayana Guru equates cause and effect and equates the Self and the non-Self as cancelable into an Absolute Self of existent-subsistence-value as found in the last verse of the present chapter, he is merely adopting the same structural axiomatic and dialectical approach beginning to be recognized in the modern West. A comparison of his approach with the approach revealed in. the following extracts shows the common basis. A common methodology and epistemology for an integrated Science of the Absolute is thus sighted.
The nature of mathematical reasoning is basically axiomatic. This is referred to in the following way by a modern French thinker, Paul Foulquie:
"Mathematics is concerned with total abstractions It attempts to liberate itself completely from experience and to axiomatize itself; that is to ay, to constitute itself into an independent system, freely posited by the mind and sufficient to itself." (5)
The relation between a definition, semantics and an axiom, is brought out by Poincaré, as quoted by Foulquie:
"In this sense an axiom is a disguised definition. Constructing semantics is the same as constructing axioms." (6)
The double reference from model to structure and vice versa is under reference in the following extract from Prof. Janin's paper:
"In the stage of research the thought of the mathematician goes from the model to the structure .... On the contrary, a didactic exposition of the theory will take place in the form of an abstract axiomatization, the model being given as an application .... if one might say, it is the structure itself that becomes the model."
In regards to the validity of extrapolation, in axiomatic thinking, Prof. Janin says:
"We can thus distinguish many stages in the construction of mathematics, stages which are not clearly separated, overlapping in time and corresponding to modes of thought which coexist in the same time." (7)
The dialectical and axiomatic view of science is clearly brought out by Foulquie:
"Scientific thought is in the first place a dialogue between the a priori and the a posteriori. Philosophers have engaged themselves in polemics for centuries on the problem of the origin of knowledge. Those among them to whom the philosophic spirit was important have attributed to man ideas independent of experience, that is to say by the contact of things themselves through the intermediary of the sense organs. Before the contemporary epoch, scientific thinkers were hardly preoccupied with such problems which were being fought out between philosophers; but certain mathematicians were excepted, they ranged themselves practically within the second case and took all knowledge to have an empirical origin.
According to the dialectical conception of science, on the contrary, no knowledge is totally given either in an a priori or in an a posteriori fashion; it results from a dialogue between the a priori and the a posteriori" (8)
In Narayana Guru's work as a whole this axiomatic approach with its epistemological and methodological implications have to be kept in mind because one necessarily presupposes the other.
It will be found that there is revealed a reduction from a formalized and mechanized model to a structural living reality in this second chapter. This is carried on stage by stage in. every other chapter until we come to the end of chapter five. This second chapter could be characterized as an ontological reduction of reality.
From the sixth chapter onwards is the reverse process of a teleological construction from the living structure to the mechanistic model of reasoning, through logic, logic-physics, and semantics. The dialogue between these two reversible processes refers to the complete methodology of the work as a whole, implying both a normalization and a re-normalization. in axiomatic thought for the purposes of a Science of the Absolute. We shall have occasion to mention more detailed implications of this two-sided methodology at each stage of our discussion.
One more word before concluding this prologue of Methodology:
We have traveled from schematic structuralism, the elements of which were laid in the Cartesian correlated or coordinates. Spinoza, Leibniz and Kant had these or similar conjugated correlate or coordinating features in their minds, to which Bergson only added his touch of vital dynamism.
A relativist dummy was needed to give to the Absolute its fully independent or non-relativist status, as Eddington pointed out in recommending his selective and subjective structuralism. Our own attempts to build up a protolinguistic language for Unified Science, adopted the readymade structure available in the colour solid to which we referred in the Preliminaries. A colourful expanse of a visible world is structurally related to a "frame" in the passage by Bergson. which we have quoted above on pages 148-153. Bergson has further improved on this initial structural image used by him above, on pages 323, 327, and 356-357. A Gaussian curve of probability, treated together with a similar one of possibility in life events or functions are referred to elsewhere.
The careful student desiring to get the special benefit of all the special features of our approach to the Science of the Absolute would do well to re-examine these pages and to relate them to similar confirmatory reference in the Upanishads and Brahma Sutras cited in the later chapters of this work. Life is thus understood as a pulsation that propagates itself in space and time and subject to a universal principle of causality at its core. When this is understood in the light of the new idioms brought into scientific thinking - such as entropy, negentropy, retroaction, osmosis, endosmosis, reciprocity, complementarity, one-to-one correspondence or cancellability of counterparts or ensembles; it will open up new and interesting vistas and instruments of research, full of beauty, promise and power in the cause of the Truth that shall make us free. The answer to such problems as materialization or psychic powers will be covered thus globally, if not in piecemeal fashion.
Before leaving behind this long apparent digression in which we have tried to see how Bergson as a modern philosopher is able to revise relativism in terms generally acceptable to philosophy, to pass on to a final section on axiomatic thinking coming into the methodology of modern science, by way of apology for taking such liberties equally trying on the reader, it might be permissible to explain here that the normative absolute is not meant to be a mere mathematical abstraction.
The last sentence quoted from Bergson above could seem to suggest that the analytical geometry of Descartes and the new way in physics of Einstein were both empty of significant or substantial content in terms of a human life that is actually lived and for which all science or philosophy is meant to be a guide or consolation through certitude.
Both Kant and Descartes agreed in their faith in schematic aids to thought and Bergson too gave to this visualized way in language his own schematized basis, revised and restated in more vital terms. Thus from Descartes through Kant, Bergson and Eddington to the modern Bourbakians, a schematic protolinguism as an aid to scientific communicability without frontiers of local vernaculars is to be recognized.
In the place of S and S' as rival systems where Peter's or Paul's consciousness would recognize one unique and universal Time, we could think of the domains proper to physics and metaphysics as capable of being represented by a common. Schema integrating both into one high human. value factor, existing and subsisting as a normative Absolute in human consciousness:
Thus it would be possible and legitimate to think of two rival Selves instead of two rival systems as Bergson had done. One of these Selves could belong to a radical, rigid, or horizontal world, and the other to a refined or verticalized order. The ontological Self could thus be the real basis of the teleological non-Self and be considered as its cause. When the negative way proper to the neti, neti approach of Vedantic methodology is thought of at this point, it would be easy for the reader to see readily how our long detour into Bergsonianism is more than justified by the common character of absolutist ontological reduction underlying the methodology of the Guru Narayana himself, as we shall presently see. These common methodological assumptions and presuppositions culminate in the fully axiomatic way of reasoning, now becoming more and more acceptable to scientific thinkers of the present day.
 Rune´s "Dictionary of Philosophy", Bombay: Jaico Publ., 1957, p.196
 Rune´s p.196
 "Search for a Norm in Western Thought", Values
 "La Dialectique", Paris: Presses Universitaires de France, 1959, p.93, our translation.
 From Prof. Janin's personal lecture notes, entitled "Rigour, Adequacy and Vigour in Axiomatic Physics."